Navigation with a safe longitudinal distance

ABSTRACT

Systems and methods are provided for navigating a host vehicle. A processing device may be programmed to receive an image representative of an environment of the host vehicle; determine a planned navigational action for the host vehicle; analyze the image to identify a target vehicle travelling toward the host vehicle; determine a next-state distance between the host vehicle and the target vehicle that would result if the planned navigational action taken; determine a stopping distance for the host vehicle based on a braking rate, a maximum acceleration capability, and a current speed of the host vehicle; determine a stopping distance for the target vehicle based on a braking rate, a maximum acceleration capability, and a current speed of the target vehicle; and implement the planned navigational action if the determined next-state distance is greater than a sum of the stopping distances for the host vehicle and the target vehicle.

CROSS REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of priority of U.S. ProvisionalPatent Application No. 62/718,554, filed on Aug. 14, 2018; U.S.Provisional Patent Application No. 62/724,355, filed on Aug. 29, 2018;U.S. Provisional Patent Application No. 62/772,366, filed on Nov. 28,2018; and U.S. Provisional Patent Application No. 62/777,914, filed onDec. 11, 2018. All of the foregoing applications are incorporated hereinby reference in their entirety.

BACKGROUND Technical Field

The present disclosure relates generally to autonomous vehiclenavigation. Additionally, this disclosure relates to systems and methodsfor navigating according to potential accident liability constraints.

Background Information

As technology continues to advance, the goal of a fully autonomousvehicle that is capable of navigating on roadways is on the horizon.Autonomous vehicles may need to take into account a variety of factorsand make appropriate decisions based on those factors to safely andaccurately reach an intended destination. For example, an autonomousvehicle may need to process and interpret visual information (e.g.,information captured from a camera), information from radar or lidar,and may also use information obtained from other sources (e.g., from aGPS device, a speed sensor, an accelerometer, a suspension sensor,etc.). At the same time, in order to navigate to a destination, anautonomous vehicle may also need to identify its location within aparticular roadway (e.g., a specific lane within a multi-lane road),navigate alongside other vehicles, avoid obstacles and pedestrians,observe traffic signals and signs, travel from one road to another roadat appropriate intersections or interchanges, and respond to any othersituation that occurs or develops during the vehicle's operation.Moreover, the navigational system may need to adhere to certain imposedconstraints. In some cases, those constraints may relate to interactionsbetween a host vehicle and one or more other objects, such as othervehicles, pedestrians, etc. In other cases, the constraints may relateto liability rules to be followed in implementing one or morenavigational actions for a host vehicle.

In the field of autonomous driving, there are two importantconsiderations for viable autonomous vehicle systems. The first is astandardization of safety assurance, including requirements that everyself-driving car must satisfy to ensure safety, and how thoserequirements can be verified. The second is scalability, as engineeringsolutions that lead to unleashed costs will not scale to millions ofcars and may prevent widespread or even not so widespread adoption ofautonomous vehicles. Thus, there is a need for an interpretable,mathematical model for safety assurance and a design of a system thatadheres to safety assurance requirements while being scalable tomillions of cars.

SUMMARY

Embodiments consistent with the present disclosure provide systems andmethods for autonomous vehicle navigation. The disclosed embodiments mayuse cameras to provide autonomous vehicle navigation features. Forexample, consistent with the disclosed embodiments, the disclosedsystems may include one, two, or more cameras that monitor theenvironment of a vehicle. The disclosed systems may provide anavigational response based on, for example, an analysis of imagescaptured by one or more of the cameras. The navigational response mayalso take into account other data including, for example, globalpositioning system (GPS) data, sensor data (e.g., from an accelerometer,a speed sensor, a suspension sensor, etc.), and/or other map data.

In an embodiment, a system for navigating a host vehicle is disclosed.The system may comprise at least one processing device programmed toreceive, from an image capture device, at least one image representativeof an environment of the host vehicle; determine, based on at least onedriving policy, a planned navigational action for accomplishing anavigational goal of the host vehicle; analyze the at least one image toidentify a target vehicle in the environment of the host vehicle,wherein a direction of travel of the target vehicle is toward the hostvehicle; determine a next-state distance between the host vehicle andthe target vehicle that would result if the planned navigational actionwas taken; determine a host vehicle braking rate, a host vehicle maximumacceleration capability, and a current speed of the host vehicle;determine a stopping distance for the host vehicle based on the hostvehicle braking rate, the host vehicle maximum acceleration capability,and the current speed of the host vehicle; determine a current speed ofthe target vehicle, a target vehicle maximum acceleration capability,and a target vehicle braking rate; determine a stopping distance for thetarget vehicle based on the target vehicle braking rate, the targetvehicle maximum acceleration capability, and the current speed of thetarget vehicle; and implement the planned navigational action if thedetermined next-state distance is greater than a sum of the stoppingdistance for the host vehicle and the stopping distance of the targetvehicle.

In an embodiment, a method for navigating a host vehicle is disclosed.The method may comprise receiving, from an image capture device, atleast one image representative of an environment of the host vehicle;determining, based on at least one driving policy, a plannednavigational action for accomplishing a navigational goal of the hostvehicle; analyzing the at least one image to identify a target vehiclein the environment of the host vehicle, wherein a direction of travel ofthe target vehicle is toward the host vehicle; determining a next-statedistance between the host vehicle and the target vehicle that wouldresult if the planned navigational action was taken; determining a hostvehicle braking rate, a host vehicle maximum acceleration capability,and a current speed oldie host vehicle; determining a stopping distancefor the host vehicle based on the host vehicle braking rate, the hostvehicle maximum acceleration capability, and the current speed of thehost vehicle; determining a current speed of the target vehicle, atarget vehicle maximum acceleration capability, and a target vehiclebraking rate; determining a stopping distance for the target vehiclebased on the target vehicle braking rate, the target vehicle maximumacceleration capability, and the current speed of the target vehicle;and implementing the planned navigational action if the determinednext-state distance is greater than a sum of the stopping distance forthe host vehicle and the stopping distance of the target vehicle.

In an embodiment, a system for navigating a host vehicle is disclosed.The system may comprise at least one processing device programmed toreceive, from an image capture device, at least one image representativeof an environment of the host vehicle; determine, based on at least onedriving policy, a planned navigational action for accomplishing anavigational goal of the host vehicle; analyze the at least one image toidentify a target vehicle in the environment of the host vehicle;determine a next-state lateral distance between the host vehicle and thetarget vehicle that would result if the planned navigational action wastaken; determine a maximum yaw rate capability of the host vehicle, amaximum change in turn radius capability of the host vehicle, and acurrent lateral speed of the host vehicle; determine a lateral brakingdistance for the host vehicle based on the maximum yaw rate capabilityof the host vehicle, the maximum change in turn radius capability of thehost vehicle, and the current lateral speed of the host vehicle;determine a current lateral speed of the target vehicle, a targetvehicle maximum yaw rate capability, and a target vehicle maximum changein turn radius capability; determine a lateral braking distance for thetarget vehicle based on the current lateral speed of the target vehicle,the target vehicle maximum yaw rate capability, and the target vehiclemaximum change in turn radius capability; and implement the plannednavigational action if the determined next-state lateral distance isgreater than a sum of the lateral braking distance for the host vehicleand the lateral braking distance of the target vehicle.

In an embodiment, a method for navigating a host vehicle is disclosed.The method may comprise receiving, from an image capture device, atleast one image representative of an environment of the host vehicle;determining, based on at least one driving policy, a plannednavigational action for accomplishing a navigational goal of the hostvehicle; analyzing the at least one image to identify a target vehiclein the environment of the host vehicle; determining a next-state lateraldistance between the host vehicle and the target vehicle that wouldresult if the planned navigational action was taken; determining amaximum yaw rate capability of the host vehicle, a maximum change inturn radius capability of the host vehicle, and a current lateral speedof the host vehicle; determining a lateral braking distance for the hostvehicle based on the maximum yaw rate capability of the host vehicle,the maximum change in turn radius capability of the host vehicle, andthe current lateral speed of the host vehicle; determining a currentlateral speed of the target vehicle, a target vehicle maximum yaw ratecapability, and a target vehicle maximum change in turn radiuscapability; determining a lateral braking distance for the targetvehicle based on the current lateral speed of the target vehicle, thetarget vehicle maximum yaw rate capability, and the target vehiclemaximum change in turn radius capability; and implementing the plannednavigational action if the determined next-state lateral distance isgreater than a sum of the lateral braking distance for the host vehicleand the lateral braking distance of the target vehicle.

In an embodiment, a system for navigating a host vehicle in proximity toa pedestrian crosswalk is disclosed. The system may comprise at leastone processing device programmed to: receive, from an image capturedevice, at least one image representative of an environment of the hostvehicle; detect, based on analysis of the at least one image, arepresentation of a pedestrian crosswalk in the at least one image;determine, based on analysis of the at least one image, whether arepresentation of a pedestrian appears in the at least one image; detecta presence of a traffic light in the environment of the host vehicle;determine whether the detected traffic light is relevant to the hostvehicle and the pedestrian crosswalk; determine a state of the detectedtraffic light; determine, when a representation of a pedestrian appearsin the at least one image, a proximity of the pedestrian relative to thedetected pedestrian crosswalk; determine, based on at least one drivingpolicy, a planned navigational action for causing the host vehicle tonavigate relative to the detected pedestrian crosswalk, whereindetermination of the planned navigational action is further based on thedetermined state of the detected traffic light and the determinedproximity of the pedestrian relative to the detected pedestriancrosswalk; and cause one or more actuator systems of the host vehicle toimplement the planned navigational action.

In an embodiment, a method for navigating a host vehicle in proximity toa pedestrian crosswalk is disclosed. The method may comprise receiving,from an image capture device, at least one image representative of anenvironment of the host vehicle; detecting, based on analysis of the atleast one image, a representation of a pedestrian crosswalk in the atleast one image; determining, based on analysis of the at least oneimage, whether a representation of a pedestrian appears in the at leastone image; detecting a presence of a traffic light in the environment ofthe host vehicle; determining whether the detected traffic light isrelevant to the host vehicle and the pedestrian crosswalk; determining astate of the detected traffic light; determining, when a representationof a pedestrian appears in the at least one image, a proximity of thepedestrian relative to the detected pedestrian crosswalk; determining,based on at least one driving policy, a planned navigational action forcausing the host vehicle to navigate relative to the detected pedestriancrosswalk, wherein determination of the planned navigational action isfurther based on the determined state of the detected traffic light andthe determined proximity of the pedestrian relative to the detectedpedestrian crosswalk; and causing one or more actuator systems of thehost vehicle to implement the planned navigational action.

In an embodiment, a method for navigating a host vehicle in proximity toa pedestrian crosswalk is disclosed. The method may comprise receiving,from an image capture device, at least one image representing anenvironment of the host vehicle; detecting a starting and an endinglocation of a crosswalk; determining, based on an analysis of the atleast one image, whether a pedestrian is present in a proximity of thecrosswalk; detecting a presence of a traffic light in the environment ofthe host vehicle; determining whether the traffic light is relevant tothe host vehicle and the crosswalk; determining a state of the trafficlight; determining a navigational action for the host vehicle invicinity of the detected crosswalk, based on: the relevancy of thetraffic light; the determined state of the traffic light; a presence ofthe pedestrian in the proximity of the crosswalk; a shortest distanceselected between the pedestrian and one of the starting or the endinglocation of the crosswalk; and a motion vector of the pedestrian; andcausing one or more actuator systems of the host vehicle to implementthe navigational action.

Consistent with other disclosed embodiments, non-transitorycomputer-readable storage media may store program instructions, whichare executable by at least one processing device and perform any of thesteps and/or methods described herein.

The foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of theclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this disclosure, illustrate various disclosed embodiments. Inthe drawings:

FIG. 1 is a diagrammatic representation of an exemplary systemconsistent with the disclosed embodiments.

FIG. 2A is a diagrammatic side view representation of an exemplaryvehicle including a system consistent with the disclosed embodiments.

FIG. 2B is a diagrammatic top view representation of the vehicle andsystem shown in FIG. 2A consistent with the disclosed embodiments.

FIG. 2C is a diagrammatic top view representation of another embodimentof a vehicle including a system consistent with the disclosedembodiments.

FIG. 2D is a diagrammatic top view representation of yet anotherembodiment of a vehicle including a system consistent with the disclosedembodiments.

FIG. 2E is a diagrammatic top view representation of yet anotherembodiment of a vehicle including a system consistent with the disclosedembodiments.

FIG. 2F is a diagrammatic representation of exemplary vehicle controlsystems consistent with the disclosed embodiments,

FIG. 3A is a diagrammatic representation of an interior of a vehicleincluding a rearview mirror and a user interface for a vehicle imagingsystem consistent with the disclosed embodiments.

FIG. 3B is an illustration of an example of a camera mount that isconfigured to be positioned behind a rearview mirror and against avehicle windshield consistent with the disclosed embodiments.

FIG. 3C is an illustration of the camera mount shown in FIG. 3B from adifferent perspective consistent with the disclosed embodiments.

FIG. 3D is an illustration of an example of a camera mount that isconfigured to be positioned behind a rearview mirror and against avehicle windshield consistent with the disclosed embodiments.

FIG. 4 is an exemplary block diagram of a memory configured to storeinstructions for performing one or more operations consistent with thedisclosed embodiments.

FIG. 5A is a flowchart showing an exemplary process for causing one ormore navigational responses based on monocular image analysis consistentwith disclosed embodiments.

FIG. 5B is a flowchart showing an exemplary process for detecting one ormore vehicles and/or pedestrians in a set of images consistent with thedisclosed embodiments.

FIG. 5C is a flowchart showing an exemplary process for detecting roadmarks and/or lane geometry information in a set of images consistentwith the disclosed embodiments.

FIG. 5D is a flowchart showing an exemplary process for detectingtraffic lights in a set of images consistent with the disclosedembodiments,

FIG. 5E is a flowchart showing an exemplary process for causing one ormore navigational responses based on a vehicle path consistent with thedisclosed embodiments.

FIG. 5F is a flowchart showing an exemplary process for determiningwhether a leading vehicle is changing lanes consistent with thedisclosed embodiments.

FIG. 6 is a flowchart showing an exemplary process for causing one ormore navigational responses based on stereo image analysis consistentwith the disclosed embodiments.

FIG. 7 is a flowchart showing an exemplary process for causing one ormore navigational responses based on an analysis of three sets of imagesconsistent with the disclosed embodiments.

FIG. 8 is a block diagram representation of modules that may beimplemented by one or more specifically programmed processing devices ofa navigation system for an autonomous vehicle consistent with thedisclosed embodiments.

FIG. 9 is a navigation options graph consistent with the disclosedembodiments.

FIG. 10 is a navigation options graph consistent with the disclosedembodiments.

FIGS. 11A, 11B, and 11C provide a schematic representation ofnavigational options of a host vehicle in a merge zone consistent withthe disclosed embodiments.

FIG. 11D provide a diagrammatic depiction of a double merge scenarioconsistent with the disclosed embodiments.

FIG. 11E provides an options graph potentially useful in a double mergescenario consistent with the disclosed embodiments.

FIG. 12 provides a diagram of a representative image captured of anenvironment of a host vehicle, along with potential navigationalconstraints consistent with the disclosed embodiments.

FIG. 13 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 14 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 15 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 16 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIGS. 17A and 17B provide a diagrammatic illustration of a host vehiclenavigating into a roundabout consistent with the disclosed embodiments.

FIG. 18 provides an algorithmic flow chart for navigating a vehicleconsistent with the disclosed embodiments.

FIG. 19 illustrates an example of a host vehicle driving on a multi-lanehighway consistent with the disclosed embodiments.

FIGS. 20A and 20B illustrate examples of a vehicle cutting in in frontof another vehicle consistent with the disclosed embodiments.

FIG. 21 illustrates an example of a vehicle following another vehicleconsistent with the disclosed embodiments.

FIG. 22 illustrates an example of a vehicle exiting a parking lot andmerging into a possibly busy road consistent with the disclosedembodiments.

FIG. 23 illustrates a vehicle traveling on a road consistent with thedisclosed embodiments.

FIGS. 24A-24D illustrate four example scenarios consistent with thedisclosed embodiments.

FIG. 25 illustrates an example scenario consistent with the disclosedembodiments.

FIG. 26 illustrates an example scenario consistent with the disclosedembodiments.

FIG. 27 illustrates an example scenario consistent with the disclosedembodiments.

FIGS. 28A and 28B illustrate an example of a scenario in which a vehicleis following another vehicle consistent with the disclosed embodiments.

FIGS. 29A and 29B illustrate example blame in cut-in scenariosconsistent with the disclosed embodiments.

FIGS. 30A and 30B illustrate example blame in cut-in scenariosconsistent with the disclosed embodiments.

FIGS. 31A-31D illustrate example blame in drifting scenarios consistentwith the disclosed embodiments.

FIGS. 32A and 32B illustrate example blame in two-way traffic scenariosconsistent with the disclosed embodiments.

FIGS. 33A and 33B illustrate example blame in two-way traffic scenariosconsistent with the disclosed embodiments.

FIGS. 34A and 34B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 35A and 35B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 36A and 36B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 37A and 37B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 38A and 38B illustrate example blame in route priority scenariosconsistent with the disclosed embodiments.

FIGS. 39A and 39B illustrate example blame in route priority scenariosconsistent the disclosed embodiments.

FIGS. 40A and 40B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 41A and 41B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 42A and 42B illustrate example blame in traffic light scenariosconsistent with the disclosed embodiments.

FIGS. 43A-43C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 44A-44C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 45A-45C illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIGS. 46A-46D illustrate example vulnerable road users (VRUs) scenariosconsistent with the disclosed embodiments.

FIG. 47A is an illustration of blame time and proper responses,consistent with the disclosed embodiments.

FIG. 47B is an illustration of route priority for routes of differinggeometries, consistent with the disclosed embodiments.

FIG. 47C is an illustration of longitudinal ordering on routes ofdiffering geometries, consistent with the disclosed embodiments.

FIG. 47D is an illustration of safe longitudinal distance betweenvehicles, consistent with the disclosed embodiments.

FIG. 47E is an illustration of a situation in which a vehicle cannotpredict the path of another vehicle, consistent with the disclosedembodiments.

FIG. 47F is an illustration of route priority at a traffic light,consistent with the disclosed embodiments.

FIG. 47G is art illustration of exemplary unstructured routes,consistent with the disclosed embodiments.

FIG. 47H is an illustration of exemplary lateral behavior in anunstructured situation, consistent with the disclosed embodiments.

FIG. 47I is an illustration of exposure time and blame time at an areaof occlusion, consistent with the disclosed embodiments.

FIG. 48A illustrates an example scenario of two vehicles traveling inopposite directions consistent with the disclosed embodiments.

FIG. 48B illustrates an example of a target vehicle traveling towards ahost vehicle consistent with the disclosed embodiments.

FIG. 49 illustrates an example of host vehicle maintaining a safelongitudinal distance consistent with the disclosed embodiments.

FIGS. 50A and 50B provide a flowchart depicting an exemplary process formaintaining a safe longitudinal distance consistent with the disclosedembodiments.

FIG. 51A illustrates an example scenario with two vehicles spacedlaterally from each other consistent with the disclosed embodiments.

FIG. 51B illustrates an example of host vehicle maintaining a safelateral distance consistent with the disclosed embodiments.

FIG. 52A illustrates an example of a host vehicle performing a plannednavigation action consistent with the disclosed embodiments.

FIG. 52B shows an example of a host vehicle determining whether toperform a navigation action.

FIGS. 53A and 53B provide a flowchart depicting an example process formaintaining a safe lateral distance consistent with the disclosedembodiments.

FIG. 54 is a schematic illustration of a roadway including crosswalks,consistent with the disclosed embodiments.

FIGS. 55A and 55B are schematic diagrams of possible navigationalactions executed by vehicles traveling along a roadway, consistent withthe disclosed embodiments.

FIGS. 55C and 55D show examples of estimating a distance from apedestrian to a crosswalk, consistent with the disclosed embodiments.

FIG. 56 is a flowchart describing a process of navigating a vehicle inthe proximity of a crosswalk, consistent with the disclosed embodiments.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawings.Wherever possible, the same reference numbers are used in the drawingsand the following description to refer to the same or similar parts.While several illustrative embodiments are described herein,modifications, adaptations and other implementations are possible. Forexample, substitutions, additions or modifications may be made to thecomponents illustrated in the drawings, and the illustrative methodsdescribed herein may be modified by substituting, reordering, removing,or adding steps to the disclosed methods. Accordingly, the followingdetailed description is not limited to the disclosed embodiments andexamples. Instead, the proper scope is defined by the appended claims.

Autonomous Vehicle Overview

As used throughout this disclosure, the term “autonomous vehicle” refersto a vehicle capable of implementing at least one navigational changewithout driver input. A “navigational change” refers to a change in oneor more of steering, braking, or acceleration/deceleration of thevehicle. To be autonomous, a vehicle need not be fully automatic (e.g.,fully operational without a driver or without driver input). Rather, anautonomous vehicle includes those that can operate under driver controlduring certain time periods and without driver control during other timeperiods. Autonomous vehicles may also include vehicles that control onlysome aspects of vehicle navigation, such as steering (e.g., to maintaina vehicle course between vehicle lane constraints) or some steeringoperations under certain circumstances (but not under allcircumstances), but may leave other aspects to the driver (e.g., brakingor braking under certain circumstances). In some cases, autonomousvehicles may handle some or all aspects of braking, speed control,and/or steering of the vehicle.

As human drivers typically rely on visual cues and observations in orderto control a vehicle, transportation infrastructures are builtaccordingly, with lane markings, traffic signs, and traffic lightsdesigned to provide visual information to drivers. In view of thesedesign characteristics of transportation infrastructures, an autonomousvehicle may include a camera and a processing unit that analyzes visualinformation captured from the environment of the vehicle. The visualinformation may include, for example, images representing components ofthe transportation infrastructure (e.g., lane markings, traffic signs,traffic lights, etc.) that are observable by drivers and other obstacles(e.g., other vehicles, pedestrians, debris, etc.). Additionally, anautonomous vehicle may also use stored information, such as informationthat provides a model of the vehicle's environment when navigating. Forexample, the vehicle may use GPS data, sensor data (e.g., from anaccelerometer, a speed sensor, a suspension sensor, etc.), and/or othermap data to provide information related to its environment while it istraveling, and the vehicle (as well as other vehicles) may use theinformation to localize itself on the model. Some vehicles can also becapable of communication among them, sharing information, altering thepeer vehicle of hazards or changes in the vehicles' surroundings, etc.

System Overview

FIG. 1 is a block diagram representation of a system 100 consistent withthe exemplary disclosed embodiments. System 100 may include variouscomponents depending on the requirements of a particular implementation.In some embodiments, system 100 may include a processing unit 110, animage acquisition unit 120, a position sensor 130, one or more memoryunits 140, 150, a map database 160, a user interface 170, and a wirelesstransceiver 172. Processing unit 110 may include one or more processingdevices. In some embodiments; processing unit 110 may include anapplications processor 180, an image processor 190, or any othersuitable processing device. Similarly, image acquisition unit 120 mayinclude any number of image acquisition devices and components dependingon the requirements of a particular application. In some embodiments,image acquisition unit 120 may include one or more image capture devices(e.g., cameras, CCDs, or any other type of image sensor), such as imagecapture device 122, image capture device 124, and image capture device126. System 100 may also include a data interface 128 communicativelyconnecting processing unit 110 to image acquisition unit 120. Forexample, data interface 128 may include any wired and/or wireless linkor links for transmitting image data acquired by image acquisition unit120 to processing unit 110.

Wireless transceiver 172 may include one or more devices configured toexchange transmissions over an air interface to one or more networks(e.g., cellular, the Internet, etc.) by use of a radio frequency,infrared frequency, magnetic field, or an electric field. Wirelesstransceiver 172 may use any known standard to transmit and/or receivedata (e.g., Wi-Fi, Bluetooth®, Bluetooth Smart, 802.15.4, ZigBee, etc.).Such transmissions can include communications from the host vehicle toone or more remotely located servers. Such transmissions may alsoinclude communications (one-way or two-way) between the host vehicle andone or more target vehicles in an environment of the host vehicle (e.g.,to facilitate coordination of navigation of the host vehicle in view ofor together with target vehicles in the environment of the hostvehicle), or even a broadcast transmission to unspecified recipients ina vicinity of the transmitting vehicle.

Both applications processor 180 and image processor 190 may includevarious types of hardware-based processing devices. For example, eitheror both of applications processor 180 and image processor 190 mayinclude a microprocessor, preprocessors (such as an image preprocessor),graphics processors, a central processing unit (CPU), support circuits,digital signal processors, integrated circuits, memory, or any othertypes of devices suitable for running applications and for imageprocessing and analysis. In some embodiments, applications processor 180and/or image processor 190 may include any type of single or multi-coreprocessor, mobile device microcontroller, central processing unit, etc.Various processing devices may be used, including, for example,processors available from manufacturers such as Intel®, AMD®, etc. andmay include various architectures (e.g., x86 processor, ARM®, etc.).

In some embodiments, applications processor 180 and/or image processor190 may include any of the EyeQ series of processor chips available fromMobileye®. These processor designs each include multiple processingunits with local memory and instruction sets. Such processors mayinclude video inputs for receiving image data from multiple imagesensors and may also include video out capabilities. In one example, theEyeQ2® uses 90 nm-micron technology operating at 332 Mhz. The EyeQ2®architecture consists of two floating point, hyper-thread 32-bit RISCCPUs (MIPS32® 34K® cores), five Vision Computing Engines (VCE), threeVector Microcode Processors (VMP®), Denali 64-bit Mobile DDR Controller,128-bit internal Sonics Interconnect, dual 16-bit Video input and 18-bitVideo output controllers, 16 channels DMA and several peripherals. TheMIPS34K CPU manages the five VCEs, three VMP™ and the DMA, the secondMIPS34K CPU and the multi-channel DMA as well as the other peripherals.The five VCEs, three VMP® and the MIPS34K CPU can perform intensivevision computations required by multi-function bundle applications. Inanother example, the EyeQ3®, which is a third generation processor andis six times more powerful that the EyeQ2®, may be used in the disclosedembodiments, in other examples, the EyeQ4® and/or the EyeQ5® may be usedin the disclosed embodiments. Of course, any newer or future EyeQprocessing devices may also be used together with the disclosedembodiments.

Any of the processing devices disclosed herein may be configured toperform certain functions. Configuring a processing device, such as anyof the described EyeQ processors or other controller or microprocessor,to perform certain functions may include programming of computerexecutable instructions and making those instructions available to theprocessing device for execution during operation of the processingdevice. In some embodiments, configuring a processing device may includeprogramming the processing device directly with architecturalinstructions. In other embodiments, configuring a processing device mayinclude storing executable instructions on a memory that is accessibleto the processing device during operation. For example, the processingdevice may access the memory to obtain and execute the storedinstructions during operation. In either case, the processing deviceconfigured to perform the sensing, image analysis, and/or navigationalfunctions disclosed herein represents a specialized hardware-basedsystem in control of multiple hardware based components of a hostvehicle.

While FIG. 1 depicts two separate processing devices included inprocessing unit 110, more or fewer processing devices may be used. Forexample, in some embodiments, a single processing device may be used toaccomplish the tasks of applications processor 180 and image processor190. In other embodiments, these tasks may be performed by more than twoprocessing devices. Further, in some embodiments, system 100 may includeone or more of processing unit 110 without including other components,such as image acquisition unit 120.

Processing unit 110 may comprise various types of devices. For example,processing unit 110 may include various devices, such as a controller,an image preprocessor, a central processing unit (CPU), supportcircuits, digital signal processors, integrated circuits, memory, or anyother types of devices for image processing and analysis. The imagepreprocessor may include a video processor for capturing, digitizing andprocessing the imagery from the image sensors. The CPU may comprise anynumber of microcontrollers or microprocessors. The support circuits maybe any number of circuits generally well known in the art, includingcache, power supply, clock and input-output circuits. The memory maystore software that, when executed by the processor, controls theoperation of the system. The memory may include databases and imageprocessing software. The memory may comprise any number of random accessmemories, read only memories, flash memories, disk drives, opticalstorage, tape storage, removable storage and other types of storage. Inone instance, the memory may be separate from the processing unit 110.In another instance, the memory may be integrated into the processingunit 110.

Each memory 140, 150 may include software instructions that whenexecuted by a processor (e.g., applications processor 180 and/or imageprocessor 190), may control operation of various aspects of system 100.These memory units may include various databases and image processingsoftware, as well as a trained system, such as a neural network, or adeep neural network, for example. The memory units may include randomaccess memory, read only memory, flash memory, disk drives, opticalstorage, tape storage, removable storage and/or any other types ofstorage. In some embodiments, memory units 140, 150 may be separate fromthe applications processor 180 and/or image processor 190. In otherembodiments, these memory units may be integrated into applicationsprocessor 180 and/or image processor 190.

Position sensor 130 may include any type of device suitable fordetermining a location associated with at least one component of system100. In some embodiments, position sensor 130 may include a UPSreceiver. Such receivers can determine a user position and velocity byprocessing signals broadcasted by global positioning system satellites.Position information from position sensor 130 may be made available toapplications processor 180 and/or image processor 190.

In some embodiments, system 100 may include components such as a speedsensor (e.g., a speedometer) for measuring a speed of vehicle 200.System 100 may also include one or more accelerometers (either singleaxis or multiaxis) for measuring accelerations of vehicle 200 along oneor more axes.

The memory units 140, 150 may include a database, or data organized inany other form, that indication a location of known landmarks. Sensoryinformation (such as images, radar signal, depth information from lidaror stereo processing of two or more images) of the environment may beprocessed together with position information, such as a GPS coordinate,vehicle's ego motion, etc. to determine a current location of thevehicle relative to the known landmarks, and refine the vehiclelocation. Certain aspects of this technology are included in alocalization technology known as REM™, which is being marketed by theassignee of the present application.

User interface 170 may include any device suitable for providinginformation to or for receiving inputs from one or more users of system100. In some embodiments, user interface 170 may include user inputdevices, including, for example, a touchscreen, microphone, keyboard,pointer devices, track wheels, cameras, knobs, buttons, etc. With suchinput devices, a user may be able to provide information inputs orcommands to system 100 by typing instructions or information, providingvoice commands, selecting menu options on a screen using buttons,pointers, or eye-tracking capabilities, or through any other suitabletechniques for communicating information to system 100.

User interface 170 may be equipped with one or more processing devicesconfigured to provide and receive information to or from a user andprocess that information for use by, for example, applications processor180. In some embodiments, such processing devices may executeinstructions for recognizing and tracking eye movements, receiving andinterpreting voice commands, recognizing and interpreting touches and/orgestures made on a touchscreen, responding to keyboard entries or menuselections, etc. In some embodiments, user interface 170 may include adisplay, speaker, tactile device, and/or any other devices far providingoutput information to a user.

Map database 160 may include any type of database for storing map datauseful to system 100. In some embodiments, map database 160 may includedata relating to the position, in a reference coordinate system, ofvarious items, including roads, water features, geographic features,businesses, points of interest, restaurants, gas stations, etc. Mapdatabase 160 may store not only the locations of such items, but alsodescriptors relating to those items, including, for example, namesassociated with any of the stored features. In some embodiments, mapdatabase 160 may be physically located with other components of system100. Alternatively or additionally, map database 160 or a portionthereof may be located remotely with respect to other components ofsystem 100 (e.g., processing unit 110). In such embodiments, informationfrom map database 160 may be downloaded over a wired or wireless dataconnection to a network (e.g., over a cellular network and/or theInternet, etc.). In some cases, map database 160 may store a sparse datamodel including polynomial representations of certain road features(e.g., lane markings) or target trajectories for the host vehicle. Mapdatabase 160 may also include stored representations of variousrecognized landmarks that may be used to determine or update a knownposition of the host vehicle with respect to a target trajectory. Thelandmark representations may include data fields such as landmark type,landmark location, among other potential identifiers.

Image capture devices 122, 124, and 126 may each include any type ofdevice suitable for capturing at least one image from an environment.Moreover, any number of image capture devices may be used to acquireimages for input to the image processor. Some embodiments may includeonly a single image capture device, while other embodiments may includetwo, three, or even four or more image capture devices. Image capturedevices 122, 124, and 126 will be further described with reference toFIGS. 2B-2E, below.

One or more cameras (e.g., image capture devices 122, 124, and 126) maybe part of a sensing block included on a vehicle. Various other sensorsmay be included in the sensing block, and any or all of the sensors maybe relied upon to develop a sensed navigational state of the vehicle. Inaddition to cameras (forward, sideward, rearward, etc), other sensorssuch as RADAR, LIDAR, and acoustic sensors may be included in thesensing block. Additionally, the sensing block may include one or morecomponents configured to communicate and transmit/receive informationrelating to the environment of the vehicle. For example, such componentsmay include wireless transceivers (RF, etc.) that may receive from asource remotely located with respect to the host vehicle sensor basedinformation or any other type of information relating to the environmentof the host vehicle. Such information may include sensor outputinformation, or related information, received from vehicle systems otherthan the host vehicle. In some embodiments, such information may includeinformation received from a remote computing device, a centralizedserver, etc. Furthermore, the cameras may take on many differentconfigurations: single camera units, multiple cameras, camera clusters,long FOV, short FOV, wide angle, fisheye, etc.

System 100, or various components thereof, may be incorporated intovarious different platforms. In some embodiments, system 100 may beincluded on a vehicle 200, as shown in FIG. 2A. For example, vehicle 200may be equipped with a processing unit 110 and any of the othercomponents of system 100, as described above relative to FIG. 1. Whilein some embodiments vehicle 200 may be equipped with only a single imagecapture device (e.g., camera), in other embodiments, such as thosediscussed in connection with FIGS. 2B 2E, multiple image capture devicesmay be used. For example, either of image capture devices 122 and 124 ofvehicle 200, as shown in FIG. 2A, may be part of an ADAS (AdvancedDriver Assistance Systems) imaging set.

The image capture devices included on vehicle 200 as part of the imageacquisition unit 120 may be positioned at any suitable location. In someembodiments, as shown in FIGS. 2A-2E and 3A-3C, image capture device 122may be located in the vicinity of the rearview mirror. This position mayprovide a line of sight similar to that of the driver of vehicle 200,which may aid in determining what is and is not visible to the driver.Image capture device 122 may be positioned at any location near therearview mirror, but placing image capture device 122 on the driver sideof the mirror may further aid in obtaining images representative of thedriver's field of view and/or line of sight.

Other locations for the image capture devices of image acquisition unit120 may also be used. For example, image capture device 124 may belocated on or in a bumper of vehicle 200. Such a location may beespecially suitable for image capture devices having a wide field ofview. The line of sight of bumper-located image capture devices can bedifferent from that of the driver and, therefore, the bumper imagecapture device and driver may not always see the same objects. The imagecapture devices (e.g., image capture devices 122, 124, and 126) may alsobe located in other locations. For example, the image capture devicesmay be located on or in one or both of the side mirrors of vehicle 200,on the roof of vehicle 200, on the hood of vehicle 200, on the trunk ofvehicle 200, on the sides of vehicle 200, mounted on, positioned behind,or positioned in front of any of the windows of vehicle 200, and mountedin or near light fixtures on the front and/or back of vehicle 200, etc.

In addition to image capture devices, vehicle 200 may include variousother components of system 100. For example, processing unit 110 may beincluded on vehicle 200 either integrated with or separate from anengine control unit (ECU) of the vehicle. Vehicle 200 may also beequipped with a position sensor 130, such as a GPS receiver and may alsoinclude a map database 160 and memory units 140 and 150.

As discussed earlier, wireless transceiver 172 may and/or receive dataover one or more networks (e.g., cellular networks, the Internet, etc.).For example, wireless transceiver 172 may upload data collected bysystem 100 to one or more servers, and download data from the one ormore servers. Via wireless transceiver 172, system 100 may receive, forexample, periodic or on demand updates to data stored in map database160, memory 140, and/or memory 150. Similarly, wireless transceiver 172may upload any data (e.g., images captured by image acquisition unit120, data received by position sensor 130 or other sensors, vehiclecontrol systems, etc.) from system 100 and/or any data processed byprocessing unit 110 to the one or more servers.

System 100 may upload data to a server (e.g., to the cloud) based on aprivacy level setting. For example, system 100 may implement privacylevel settings to regulate or limit the types of data (includingmetadata) sent to the server that may uniquely identify a vehicle and ordriver/owner of a vehicle. Such settings may be set by user via, farexample, wireless transceiver 172, be initialized by factory defaultsettings, or by data received by wireless transceiver 172.

In some embodiments, system 100 may upload data according to a “high”privacy level, and under setting a setting, system 100 may transmit data(e.g., location information related to a route, captured images, etc.)without any details about the specific vehicle and/or driver owner. Forexample, when uploading data according to a “high” privacy setting,system 100 may not include a vehicle identification number (VIN) or aname of a driver or owner of the vehicle, and may instead transmit data,such as captured images and/or limited location information related to aroute.

Other privacy levels are contemplated as well. For example, system. 100may transmit data to a server according to an “intermediate” privacylevel and include additional information not included under a “high”privacy level, such as a make and/or model of a vehicle and/or a vehicletype (e.g., a passenger vehicle, sport utility vehicle, truck, etc.). Insome embodiments, system 100 may upload data according to a “low”privacy level. Under a “low” privacy level setting, system 100 mayupload data and include information sufficient to uniquely identify aspecific vehicle, owner/driver, and/or a portion or entirely of a routetraveled by the vehicle. Such “low” privacy level data may include oneor more of, for example, a VIN, a driver/owner name, an originationpoint of a vehicle prior to departure, an intended destination of thevehicle, a make and/or model of the vehicle, a type of the vehicle, etc.

FIG. 2A is a diagrammatic side view representation of an exemplaryvehicle imaging system consistent with the disclosed embodiments. FIG.2B is a diagrammatic top view illustration of the embodiment shown inFIG. 2A. As illustrated in FIG. 2B, the disclosed embodiments mayinclude a vehicle 200 including in its body a system 100 with a firstimage capture device 122 positioned in the vicinity of the rearviewmirror and/or near the driver of vehicle 200, a second image capturedevice 124 positioned on or in a bumper region (e.g., one of bumperregions 210) of vehicle 200, and a processing unit 110.

As illustrated in FIG. 2C, image capture devices 122 and 124 may both bepositioned in the vicinity of the rearview mirror and/or near the driverof vehicle 200. Additionally, while two image capture devices 122 and124 are shown in FIGS. 2B and 2C, it should be understood that otherembodiments may include more than two image capture devices. Forexample, in the embodiments shown in FIGS. 2D and 2E, first, second, andthird image capture devices 122, 124, and 126, are included in thesystem 100 of vehicle 200.

As illustrated in FIG. 2D, image capture device 122 may be positioned inthe vicinity of the rearview mirror and/or near the driver of vehicle200, and image capture devices 124 and 126 may be positioned on or in abumper region (e.g., one of bumper regions 210) of vehicle 200. And asshown in FIG. 2E, image capture devices 122, 124, and 126 may bepositioned in the vicinity of the rearview mirror and/or near the driverseat of vehicle 200. The disclosed embodiments are not limited to anyparticular number and configuration of the image capture devices, andthe image capture devices may be positioned in any appropriate locationwithin and/or on vehicle 200.

It is to be understood that the disclosed embodiments are not limited tovehicles and could be applied in other contexts. It is also to beunderstood that disclosed embodiments are not limited to a particulartype of vehicle 200 and may be applicable to all types of vehiclesincluding automobiles, trucks, trailers, and other types of vehicles.

The first image capture device 122 may include any suitable type ofimage capture device. Image capture device 122 may include an opticalaxis. In one instance, the image capture device 122 may include anAptina M9V024 WVGA sensor with a global shutter. In other embodiments,image capture device 122 may provide a resolution of 1280×960 pixels andmay include a rolling shutter. Image capture device 122 may includevarious optical elements. In some embodiments one or more lenses may beincluded, for example, to provide a desired focal length and field ofview for the image capture device. In some embodiments, image capturedevice 122 may be associated with a 6 mm lens or a 12 mm lens. In someembodiments, image capture device 122 may be configured to captureimages having a desired field-of-view (FOV) 202, as illustrated in FIG.2D. For example, image capture device 122 may be configured to have aregular FOV, such as within a range of 40 degrees to 56 degrees,including a 46 degrees. FOV, 50 degree FOV, 52 degree FOV, or greater.Alternatively, image capture device 122 may be configured to have anarrow FOV in the range of 23 to 40 degrees, such as a 28 degree FOV or36 degree FOV. In addition, image capture device 122 may be configuredto have a wide FOV in the range of 100 to 180 degrees. In someembodiments, image capture device 122 may include a wide angle bumpercamera or one with up to a 180 degree FOV. In some embodiments, imagecapture device 122 may be a 7.2M pixel image capture device with anaspect ratio of about 2:1 (e.g., H×V=3800×1900 pixels) with about 100degree horizontal FOV. Such an image capture device may be used in placeof a three image capture device configuration. Due to significant lensdistortion, the vertical FOV of such an image capture device may besignificantly less than 50 degrees in implementations in which the imagecapture device uses a radially symmetric lens. For example, such a lensmay not be radially symmetric which would allow for a vertical FOVgreater than 50 degrees with 100 degree horizontal FOV.

The first image capture device 122 may acquire a plurality of firstimages relative to a scene associated with vehicle 200. Each of theplurality of first images may be acquired as a series of image scanlines, which may be captured using a rolling shutter. Each scan line mayinclude a plurality of pixels.

The first image capture device 122 may have a scan rate associated withacquisition of each of the first series of image scan lines. The scanrate may refer to a rate at which an image sensor can acquire image dataassociated with each pixel included in a particular scan line.

Image capture devices 122, 124, and 126 may contain any suitable typeand number of image sensors, including CCD sensors or CMOS sensors, forexample. In one embodiment, a CMOS image sensor may be employed alongwith a rolling shutter, such that each pixel in a row is read one at atime, and scanning of the rows proceeds on a row-by-row basis until anentire image frame has been captured. In some embodiments, the rows maybe captured sequentially from top to bottom relative to the frame.

In some embodiments, one or more of the image capture devices (e.g.,image capture devices 122, 124, and 126) disclosed herein may constitutea high resolution imager and may have a resolution greater than 5Mpixel, 7M pixel, 10M pixel, or greater.

The use of a rolling shutter may result in pixels in different rowsbeing exposed and captured at different times, which may cause skew andother image artifacts in the captured image frame. On the other hand,when the image capture device 122 is configured to operate with a globalor synchronous shutter, all of the pixels may be exposed for the sameamount of time and during a common exposure period. As a result, theimage data in a frame collected from a system employing a global shutterrepresents a snapshot of the entire FOV (such as FOV 202) at aparticular time. In contrast, in a rolling shutter application, each rowin a frame is exposed and data is capture at different times. Thus,moving objects may appear distorted in an image capture device having arolling shutter. This phenomenon will be described in greater detailbelow.

The second image capture device 124 and the third image capturing device126 may be any type of image capture device. Like the first imagecapture device 122, each of image capture devices 124 and 126 mayinclude an optical axis. In one embodiment, each of image capturedevices 124 and 126 may include an Aptina M9V024 WVGA sensor with aglobal shutter. Alternatively, each of image capture devices 124 and 126may include a rolling shutter. Like image capture device 122, imagecapture devices 124 and 126 may be configured to include various lensesand optical elements. In some embodiments, lenses associated with imagecapture devices 124 and 126 may provide FOVs (such as FOVs 204 and 206)that are the same as, or narrower than, a FOV (such as FOV 202)associated with image capture device 122. For example, image capturedevices 124 and 126 may have FOVs of 40 degrees, 30 degrees, 26 degrees,23 degrees, 20 degrees, or less.

Image capture devices 124 and 126 may acquire a plurality of second andthird images relative to a scene associated with vehicle 200. Each ofthe plurality of second and third images may be acquired as a second andthird series of image scan lines, which may be captured using a rollingshutter. Each scan line or row may have a plurality of pixels. Imagecapture devices 124 and 126 may have second and third scan ratesassociated with acquisition of each of image scan lines included in thesecond and third series.

Each image capture device 122, 124, and 126 may be positioned at anysuitable position and orientation relative to vehicle 200. The relativepositioning of the image capture devices 122, 124, and 126 may beselected to aid in fusing together the information acquired from theimage capture devices. For example, in some embodiments, a FOV (such asFOV 204) associated with image capture device 124 may overlap partiallyor fully with a FOV (such as FOV 202) associated with image capturedevice 122 and a FOV (such as FOY 206) associated with image capturedevice 126.

Image capture devices 122, 124, and 126 may be located on vehicle 200 atany suitable relative heights. In one instance, there may be a heightdifference between the image capture devices 122, 124, and 126, whichmay provide sufficient parallax information to enable stereo analysis.For example, as shown in FIG. 2A, the two image capture devices 122 and124 are at different heights. There may also be a lateral displacementdifference between image capture devices 122, 124, and 126, givingadditional parallax information for stereo analysis by processing unit110, for example. The difference in the lateral displacement may bedenoted by d_(x), as shown in FIGS. 2C and 2D. In some embodiments, foreor aft displacement (e.g., range displacement) may exist between imagecapture devices 122, 124, and 126. For example, image capture device 122may be located 0.5 to 2 meters or more behind image capture device 124and/or image capture device 126. This type of displacement may enableone of the image capture devices to cover potential blind spots of theother image capture device(s).

Image capture devices 122 may have any suitable resolution capability(e.g., number of pixels associated with the image sensor), and theresolution of the image sensor(s) associated with the image capturedevice 122 may be higher, lower, or the same as the resolution of theimage sensor(s) associated with image capture devices 124 and 126. Insome embodiments, the image sensor(s) associated with image capturedevice 122 and/or image capture devices 124 and 126 may have aresolution of 640×480, 1024×768, 1280×960, or any other suitableresolution.

The frame rate (e.g., the rate at which an image capture device acquiresa set of pixel data of one image frame before moving on to capture pixeldata associated with the next image frame) may be controllable. Theframe rate associated with image capture device 122 may be higher,lower, or the same as the frame rate associated with image capturedevices 124 and 126. The frame rate associated with image capturedevices 122, 124, and 126 may depend on a variety of factors that mayaffect the timing of the frame rate. For example, one or more of imagecapture devices 122, 124, and 126 may include a selectable pixel delayperiod imposed before or after acquisition of image data associated withone or more pixels of an image sensor in image capture device 122, 124,and/or 126. Generally, image data corresponding to each pixel may beacquired according to a clock rate for the device (e.g., one pixel perclock cycle). Additionally, in embodiments including a rolling shutter,one or more of image capture devices 122, 124, and 126 may include aselectable horizontal blanking period imposed before or afteracquisition of image data associated with a row of pixels of an imagesensor in image capture device 122, 124, and/or 126. Further, one ormore of image capture devices 122, 124, and/or 126 may include aselectable vertical blanking period imposed before or after acquisitionof image data associated with an image frame of image capture device122, 124, and 126.

These timing controls may enable synchronization of frame ratesassociated with image capture devices 122, 124, and 126, even where theLine scan rates of each are different. Additionally, as will bediscussed in greater detail below, these selectable timing controls,among other factors (e.g., image sensor resolution, maximum line scanrates, etc.) may enable synchronization of image capture from an areawhere the FOV of image capture device 122 overlaps with one or more FOVsof image capture devices 124 and 126, even where the field of view ofimage capture device 122 is different from the FOVs of image capturedevices 124 and 126.

Frame rate timing in image capture device 122, 124, and 126 may dependon the resolution of the associated image sensors. For example, assumingsimilar line scan rates for both devices, if one device includes animage sensor having a resolution of 640×480 and another device includesan image sensor with a resolution of 1280×960, then more time will berequired to acquire a frame of image data from the sensor having thehigher resolution.

Another factor that may, affect the timing of image data acquisition inimage capture devices 122, 124, and 126 is the maximum line scan rate.For example, acquisition of a row of image data from an image sensorincluded in image capture device 122, 124, and 126 will require someminimum amount of time. Assuming no pixel delay periods are added, thisminimum amount of time for acquisition of a row of image data will berelated to the maximum line scan rate for a particular device. Devicesthat offer higher maximum line scan rates have the potential to providehigher frame rates than devices with lower maximum line scan rates. Insome embodiments, one or more of image capture devices 124 and 126 mayhave a maximum line scan rate that is higher than a maximum line scanrate associated with image capture device 122. In some embodiments, themaximum line scan rate of image capture device 124 and/or 126 may be1.25, 1.5, 1.75, or 2 times or more than a maximum line scan rate ofimage capture device 122.

In another embodiment, image capture devices 122, 124, and 126 may havethe same maximum line scan rate, but image capture device 122 may beoperated at a scan rate less than or equal to its maximum scan rate. Thesystem may be configured such that one or more of image capture devices124 and 126 operate at a line scan rate that is equal to the line scanrate of image capture device 122. In other instances, the system may beconfigured such that the line scan rate of image capture device 124and/or image capture device 126 may be 1.25, 1.5, 1.75, or 2 times ormore than the line scan rate of image capture device 122.

In some embodiments, image capture devices 122, 124, and 126 may beasymmetric. That is, they may include cameras having different fields ofview (FOV) and focal lengths. The fields of view of image capturedevices 122, 124, and 126 may include any desired area relative to anenvironment of vehicle 200, for example. In some embodiments, one ormore of image capture devices 122, 124, and 126 may be configured toacquire image data from an environment in front of vehicle 200, behindvehicle 200, to the sides of vehicle 200, or combinations thereof.

Further, the focal length associated with each image capture device 122,124, and/or 126 may be selectable (e.g., by inclusion of appropriatelenses etc.) such that each device acquires images of objects at adesired distance range relative to vehicle 200. For example, in someembodiments image capture devices 122, 124, and 126 may acquire imagesof close-up objects within a few meters from the vehicle. Image capturedevices 122, 124, and 126 may also be configured to acquire images ofobjects at ranges more distant from the vehicle (e.g., 25 m, 50 m, 100m, 150 m, or more). Further, the focal lengths of image capture devices122, 124, and 126 may be selected such that one image capture device(e.g., image capture device 122) can acquire images of objectsrelatively close to the vehicle (e.g., within 10 m or within 20 m) whilethe other image capture devices (e.g., image capture devices 124 and126) can acquire images of more distant objects (e.g., greater than 20m, 50 m, 100 m, 150 m, etc.) from vehicle 200.

According to some embodiments, the FOV of one or more image capturedevices 122, 124, and 126 may have a wide angle. For example, it may beadvantageous to have a FOV of 140 degrees, especially for image capturedevices 122, 124, and 126 that may be used to capture images of the areain the vicinity of vehicle 200. For example, image capture device 122may be used to capture images of the area to the right or left ofvehicle 200 and, in such embodiments, it may be desirable for imagecapture device 122 to have a wide FOV (e.g., at least 140 degrees).

The field of view associated with each of image capture devices 122,124, and 126 may depend on the respective focal lengths. For example, asthe focal length increases, the corresponding field of view decreases.

Image capture devices 122, 124, and 126 may be configured to have anysuitable fields of view. In one particular example, image capture device122 may have a horizontal FOV of 46 degrees, image capture device 124may have a horizontal FOV of 23 degrees, and image capture device 126may have a horizontal FOV in between 23 and 46 degrees. In anotherinstance, image capture device 122 may have a horizontal FOV of 52degrees, image capture device 124 may have a horizontal FOV of 26degrees, and image capture device 126 may have a horizontal FOV inbetween 26 and 52 degrees. In some embodiments, a ratio of the FOV ofimage capture device 122 to the FOVs of image capture device 124 and/orimage capture device 126 may vary from 1.5 to 2.0. In other embodiments,this ratio may vary between 1.25 and 2.25.

System 100 may be configured so that a field of view of image capturedevice 122 overlaps, at least partially or fully, with a field of viewof image capture device 124 and/or image capture device 126. In someembodiments, system 100 may be configured such that the fields of viewof image capture devices 124 and 126, for example, fall within (e.g.,are narrower than) and share a common center with the field of view ofimage capture device 122. In other embodiments, the image capturedevices 122, 124, and 126 may capture adjacent FOVs or may have partialoverlap in their FOVs. In some embodiments, the fields of view of imagecapture devices 122, 124, and 126 may be aligned such that a center ofthe narrower FOV image capture devices 124 and/or 126 may be located ina lower half of the field of view of the wider FOV device 122.

FIG. 2F is a diagrammatic representation of exemplary vehicle controlsystems, consistent with the disclosed embodiments. As indicated in FIG.2F, vehicle 200 may include throttling system 220, braking system 230,and steering system 240. System 100 may provide inputs (e.g., controlsignals) to one or more of throttling system 220, braking system 230,and steering system 240 over one or more data links (e.g., any wiredand/or wireless link or links for transmitting data). For example, basedon analysis of images acquired by image capture devices 122, 124, and/or126, system 100 may provide control signals to one or more of throttlingsystem 220, braking system 230, and steering system 240 to navigatevehicle 200 (e.g., by causing an acceleration, a turn, a lane shift,etc.). Further, system 100 may receive inputs from one- or more ofthrottling system 220, braking system 230, and steering system 24indicating operating conditions of vehicle 200 (e.g., speed, whethervehicle 200 is braking and/or turning, etc.). Further details areprovided in connection with FIGS. 4-7, below.

As shown in FIG. 3A, vehicle 200 may also include a user interface 170for interacting with a driver or a passenger of vehicle 200. Forexample, user interface 170 in a vehicle application may include a touchscreen 320, knobs 330, buttons 340, and a microphone 350. A driver orpassenger of vehicle 200 may also use handles (e.g., located on or nearthe steering column of vehicle 200 including, for example, turn signalhandles), buttons (e.g., located on the steering wheel of vehicle 200),and the like, to interact with system 100. In some embodiments,microphone 350 may be positioned adjacent to a rearview mirror 310.Similarly, in some embodiments, image capture device 122 may be locatednear rearview mirror 310. In some embodiments, user interface 170 mayalso include one or more speakers 360 (e.g., speakers of a vehicle audiosystem). For example, system 100 may provide various notifications(e.g., alerts) via speakers 360.

FIGS. 3B-3D are illustrations of an exemplary camera mount 370configured to be positioned behind a rearview mirror (e.g., rearviewmirror 310) and against a vehicle windshield, consistent with disclosedembodiments. As shown in FIG. 3B, camera mount 370 may include imagecapture devices 122, 124, and 126. Image capture devices 124 and 126 maybe positioned behind a glare shield 380, which nay be flush against thevehicle windshield and include a composition of film and/oranti-reflective materials. For example, glare shield 380 may bepositioned such that it aligns against a vehicle windshield having amatching slope. In some embodiments, each of image capture devices 122,124, and 126 may be positioned behind glare shield 380, as depicted, forexample, in FIG. 3D. The disclosed embodiments are not limited to anyparticular configuration of image capture devices 122, 124, and 126,camera mount 370, and glare shield 380. FIG. 3C is an illustration ofcamera mount 370 shown in FIG. 3B from a front perspective.

As will be appreciated by a person skilled in the art having the benefitof this disclosure, numerous variations and/or modifications may be madeto the foregoing disclosed embodiments. For example, not all componentsare essential for the operation of system 100. Further, any componentmay be located in any appropriate part of system 100 and the componentsmay be rearranged into a variety of configurations while providing thefunctionality of the disclosed embodiments. Therefore, the foregoingconfigurations are examples and, regardless of the configurationsdiscussed above, system 100 can provide a wide range of functionality toanalyze the surroundings of vehicle 200 and navigate vehicle 200 inresponse to the analysis.

As discussed below in further detail and consistent with variousdisclosed embodiments, system 100 may provide a variety of featuresrelated to autonomous driving and/or driver assist technology. Forexample, system 100 may analyze image data, position data (e.g., GPSlocation information), map data, speed data, and/or data from sensorsincluded in vehicle 200. System 100 may collect the data for analysisfront, for example, image acquisition unit 120, position sensor 130, andother sensors. Further, system 100 may analyze the collected data todetermine whether or not vehicle 200 should take a certain action, andthen automatically take the determined action without humanintervention. For example, when vehicle 200 navigates without humanintervention, system 100 may automatically control the braking,acceleration, and/or steering of vehicle 200 (e.g., by sending controlsignals to one or more of throttling system 220, braking system 230, andsteering system 240). Further, system 100 may analyze the collected dataand issue warnings and/or alerts to vehicle occupants based on theanalysis of the collected data. Additional details regarding the variousembodiments that are provided by system 100 are provided below,

Forward-Facing Multi-Imaging System

As discussed above, system 100 may provide drive assist functionalitythat uses a multi-camera system. The multi-camera system may use one ormore cameras facing in the forward direction of a vehicle. In otherembodiments, the multi-camera system may include one or more camerasfacing to the side of a vehicle or to the rear of the vehicle. In oneembodiment, for example, system 100 may use a two-camera imaging system,where a first camera and a second camera (e.g., image capture devices122 and 124) may be positioned at the from and/or the sides of a vehicle(e.g., vehicle 200). Other camera configurations are consistent with thedisclosed embodiments, and the configurations disclosed herein areexamples. For example, system 100 may include a configuration of anynumber of cameras (e.g., one, two, three, four, five, six, seven, eight,etc.) Furthermore, system 100 may include “clusters” of cameras. Forexample, a cluster of cameras (including any appropriate number ofcameras, e.g., one, four, eight, etc.) may be forward-facing relative toa vehicle, or may be facing any other direction (e.g., reward-facing,side-facing, at an angle, etc.) Accordingly, system 100 may includemultiple clusters of cameras, with each cluster oriented in a particulardirection to capture images from a particular region of a vehicle'senvironment.

The first camera may have a field of view that is greater than, lessthan, or partially overlapping with, the field of view of the secondcamera. In addition, the first camera may be connected to a first imageprocessor to perform monocular image analysis of images provided by thefirst camera, and the second camera may be connected to a second imageprocessor to perform monocular image analysis of images provided by thesecond camera. The outputs (e.g., processed information) of the firstand second image processors may be combined. In some embodiments, thesecond image processor may receive images from both the first camera andsecond camera to perform stereo analysis. In another embodiment, system100 may use a three-camera imaging system where each of the cameras hasa different field of view. Such a system may, therefore, make decisionsbased on information derived from objects located at varying distancesboth forward and to the sides of the vehicle. References to monocularimage analysis may refer to instances where image analysis is performedbased on images captured from a single point of view (e.g., from asingle camera). Stereo image analysis may refer to instances where imageanalysis is performed based on two or more images captured with one ormore variations of an image capture parameter. For example, capturedimages suitable for performing stereo image analysis may include imagescaptured: from two or more different positions, from different fields ofview, using different focal lengths, along with parallax information,etc.

For example, in one embodiment, system 100 may implement a three cameraconfiguration using image capture devices 122-126. In such aconfiguration, image capture device 122 may provide a narrow field ofview (e.g., 34 degrees, or other values selected from a range of about20 to 45 degrees, etc.), image capture device 124 may provide a widefield of view (e.g., 150 degrees or other values selected from a rangeof about 100 to about 180 degrees), and image capture device 126 mayprovide an intermediate field of view (e.g., 46 degrees or other valuesselected from a range of about 35 to about 60 degrees). In someembodiments, image capture device 126 may act as a main or primarycamera. Image capture devices 122-126 may be positioned behind rearviewmirror 310 and positioned substantially side-by-side (e.g., 6 cm apart).Further, in some embodiments, as discussed above, one or more of imagecapture devices 122-126 may be mounted behind glare shield 380 that isflush with the windshield of vehicle 200. Such shielding may act tominimize the impact of any reflections from inside the car on imagecapture devices 122-126.

In another embodiment, as discussed above in connection with FIGS. 3Band 3C, the wide field of view camera (e.g., image capture device 124 inthe above example) may be mounted lower than the narrow and main fieldof view cameras (e.g., image devices 122 and 126 in the above example),This configuration may provide a free line of sight from the wide fieldof view camera. To reduce reflections, the cameras may be mounted closeto the windshield of vehicle 200, and may include polarizers on thecameras to damp reflected light.

A three camera system may provide certain performance characteristics.For example, some embodiments may include an ability to validate thedetection of objects by one camera based on detection results fromanother camera. In the three camera configuration discussed above,processing unit 110 may include, for example, three processing devices(e.g., three EyeQ series of processor chips, as discussed above), witheach processing device dedicated to processing images captured by one ormore of image capture devices 122-126.

In a three camera system, a first processing device may receive imagesfrom both the main camera and the narrow field of view camera, andperform vision processing of the narrow FOV camera to, for example,detect other vehicles, pedestrians, lane marks, traffic signs, trafficlights, and other road objects. Further, the first processing device maycalculate a disparity of pixels between the images from the main cameraand the narrow camera and create a 3D reconstruction of the environmentof vehicle 200. The first processing device may then combine the 3Dreconstruction with 3D map data or with 3D information calculated basedon information from another camera.

The second processing device may receive images from the main camera andperform vision processing to detect other vehicles, pedestrians, lanemarks, traffic signs, traffic lights, and other road objects.Additionally, the second processing device may calculate a cameradisplacement and, based on the displacement, calculate a disparity ofpixels between successive images and create a 3D reconstruction of thescene (e.g., a structure from motion). The second processing device maysend the structure from motion based 3D reconstruction to the firstprocessing device to be combined with the stereo 3D images.

The third processing device may receive images from the wide FOV cameraand process the images to detect vehicles, pedestrians, lane marks,traffic signs, traffic lights, and other road objects. The thirdprocessing device may further execute additional processing instructionsto analyze images to identify objects moving in the image, such asvehicles changing lanes, pedestrians, etc.

In some embodiments, having streams of image-based information capturedand processed independently may provide an opportunity for providingredundancy in the system. Such redundancy may include, for example,using a first image capture device and the images processed from thatdevice to validate and/or supplement information obtained by capturingand processing image information from at least a second image capturedevice.

In some embodiments, system 100 may use two image capture devices (e.g.,image capture devices 122 and 124) in providing navigation assistancefor vehicle 200 and use a third image capture device (e.g., imagecapture device 126) to provide redundancy and validate the analysis ofdata received from the other two image capture devices. For example, insuch a configuration, image capture devices 122 and 124 may provideimages for stereo analysis by system 100 for navigating vehicle 200,while image capture device 126 may provide images for monocular analysisby system 100 to provide redundancy and validation of informationobtained based on images captured from image capture device 122 and/orimage capture device 124. That is, image capture device 126 (and acorresponding processing device) may be considered to provide aredundant sub-system for providing a check on the analysis derived fromimage capture devices 122 and 124 (e.g., to provide an automaticemergency braking (AEB) system). Furthermore, in some embodiments,redundancy and validation of received data may be supplemented based oninformation received from one more sensors (e.g., radar, lidar, acousticsensors, information received from one or more transceivers outside of avehicle, etc.).

One of skill in the art will recognize that the above cameraconfigurations, camera placements, number of cameras, camera locations,etc., are examples only. These components and others described relativeto the overall system may be assembled and used in a variety ofdifferent configurations without departing from the scope of thedisclosed embodiments. Further details regarding usage of a multi-camerasystem to provide driver assist and/or autonomous vehicle functionalityfollow below.

FIG. 4 is an exemplary functional block diagram of memory 140 and/or150, which may be stored/programmed with instructions for performing oneor more operations consistent with the disclosed embodiments. Althoughthe following refers to memory 140, one of skill in the art willrecognize that instructions may be stored in memory 140 and/or 150.

As shown in FIG. 4, memory 140 may store a monocular image analysismodule 402, a stereo image analysis module 404, a velocity andacceleration module 406, and a navigational response module 408. Thedisclosed embodiments are not limited to any particular configuration ofmemory 140. Further, applications processor 180 and/or image processor190 may execute the instructions stored in any of modules 402-408included in memory 140. One of skill in the art will understand thatreferences in the following discussions to processing unit 110 may referto applications processor 180 and image processor 190 individually orcollectively. Accordingly, steps of any of the following processes maybe performed by one or more processing devices.

In one embodiment, monocular image analysis module 402 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs monocular image analysis of a set ofimages acquired by one of image capture devices 122, 124, and 126. Insome embodiments, processing unit 110 may combine information from a setof images with additional sensory information (e.g., information fromradar) to perform the monocular image analysis. As described inconnection with FIGS. 5A-5D below, monocular image analysis module 402may include instructions for detecting a set of features within the setof images, such as lane markings, vehicles, pedestrians, road signs,highway exit ramps, traffic lights, hazardous objects, and any otherfeature associated with an environment of a vehicle. Based on theanalysis, system 100 (e.g., via processing unit 110) may cause one ormore navigational responses in vehicle 200, such as a turn, a laneshift, a change in acceleration, and the like, as discussed below inconnection with navigational response module 408.

In one embodiment, monocular image analysis module 402 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs monocular image analysis of a set ofimages acquired by one of image capture devices 122, 124, and 126. Insome embodiments, processing unit 110 may combine information from a setof images with additional sensory information (e.g., information fromradar, lidar, etc.) to perform the monocular image analysis. Asdescribed in connection with FIGS. 5A-5D below, monocular image analysismodule 402 may include instructions for detecting a set of featureswithin the set of images, such as lane markings, vehicles, pedestrians,road signs, highway exit ramps, traffic lights, hazardous objects, andany other feature associated with an environment of a vehicle. Based onthe analysis, system 100 (e.g., via processing unit 110) may cause oneor more navigational responses in vehicle 200, such as a turn, a laneshill, a change in acceleration, and the like, as discussed below inconnection with determining a navigational response.

In one embodiment, stereo image analysis module 404 may storeinstructions (such as computer vision software) which, when executed byprocessing unit 110, performs stereo image analysis of first and secondsets of images acquired by a combination of image capture devicesselected from any of image capture devices 122, 124, and 126. In someembodiments, processing unit 110 may combine information from the firstand second sets of images with additional sensory, information (e.g.,information from radar) to perform the stereo image analysis. Forexample, stereo image analysis module 404 may include instructions forperforming stereo image analysis based on a first set of images acquiredby image capture device 124 and a second set of images acquired by imagecapture device 126. As described in connection with FIG. 6 below, stereoimage analysis module 404 may include instructions fix detecting a setof features within the first and second sets of images, such as lanemarkings, vehicles, pedestrians, road signs, highway exit ramps, trafficlights, hazardous objects, and the like. Based on the analysis,processing unit 110 may cause one or more navigational responses invehicle 200, such as a turn, a lane shift, a change in acceleration, andthe like, as discussed below in connection with navigational responsemodule 408. Furthermore, in some embodiments, stereo image analysismodule 404 may implement techniques associated with a trained system(such as a neural network or a deep neural network) or an untrainedsystem.

In one embodiment, velocity and acceleration module 406 may storesoftware configured to analyze data received from one or more computingand electromechanical devices in vehicle 200 that are configured tocause a change in velocity and/or acceleration of vehicle 200. Forexample, processing unit 110 may execute instructions associated withvelocity and acceleration module 406 to calculate a target speed forvehicle 200 based on data derived from execution of monocular imageanalysis module 402 and/or stereo image analysis module 404. Such datamay include, for example, a target position, velocity, and/oracceleration, the position and/or speed of vehicle 200 relative to anearby vehicle, pedestrian, or road object, position information forvehicle 200 relative to lane markings of the road, and the like. Inaddition, processing unit 110 may calculate a target speed for vehicle200 based on sensory input (e.g., information from radar) and input fromother systems of vehicle 200, such as throttling system 220, brakingsystem 230, and/or steering system 240 of vehicle 200. Based on thecalculated target speed, processing unit 110 may transmit electronicsignals to throttling system. 220, braking system 230, and/or steeringsystem 240 of vehicle 200 to trigger a change in velocity and/oracceleration by, for example, physically depressing the brake or easingup off the accelerator of vehicle 200.

In one embodiment, navigational response module 408 may store softwareexecutable by processing unit 110 to determine a desired navigationalresponse based on data derived from execution of monocular imageanalysis module 402 and/or stereo image analysis module 404. Such datamay include position and speed information associated with nearbyvehicles, pedestrians, and road objects, target position information forvehicle 200, and the like. Additionally, in some embodiments, thenavigational response may be based (partially or fully) on map data, apredetermined position of vehicle 200, and/or a relative velocity or arelative acceleration between vehicle 200 and one or more objectsdetected from execution of monocular image analysis module 402 and/orstereo image analysis module 404. Navigational response module 408 mayalso determine a desired navigational response based on sensory input(e.g., information from radar) and inputs from other systems of vehicle200, such as throttling system 220, braking system 230, and steeringsystem 240 of vehicle 200. Based on the desired navigational response,processing unit 110 may transmit electronic signals to throttling system220, braking system 230, and steering system 240 of vehicle 200 totrigger a desired navigational response by, for example, turning thesteering wheel of vehicle 200 to achieve a rotation of a predeterminedangle. In some embodiments, processing unit 110 may use the output ofnavigational response module 408 (e.g., the desired navigationalresponse) as an input to execution of velocity and acceleration module406 for calculating a change in speed of vehicle 200.

Furthermore, any of the modules (e.g., modules 402, 404, and 406)disclosed herein may implement techniques associated with a trainedsystem (such as a neural network or a deep neural network) or anuntrained system.

FIG. 5A is a flowchart showing an exemplary process 500A for causing oneor more navigational responses based on monocular image analysis,consistent with disclosed embodiments. At step 510, processing unit 110may receive a plurality of images via data interface 128 betweenprocessing unit 110 and image acquisition unit 120. For instance, acamera included in image acquisition unit 120 (such as image capturedevice 122 having field of view 202) may capture a plurality of imagesof an area forward of vehicle 200 (or to the sides or rear of a vehicle,for example) and transmit them over a data connection (e.g., digital,wired, USB, wireless, Bluetooth, etc.) to processing unit 110.Processing unit 110 may execute monocular image analysis module 402 toanalyze the plurality of images at step 520, as described in furtherdetail in connection with FIGS. 5B-5D below. By performing the analysis,processing unit 110 may detect a set of features within the set ofimages, such as lane markings, vehicles, pedestrians, road signs,highway exit ramps, traffic lights, and the like.

Processing unit 110 may also execute monocular image analysis module 402to detect various road hazards at step 520, such as, for example, partsof a truck tire, fallen road signs, loose cargo, small animals, and thelike. Road hazards may vary in structure, shape, size, and color, whichmay make detection of such hazards more challenging. In someembodiments, processing unit 110 may execute monocular image analysismodule 402 to perform multi-frame analysis on the plurality of images todetect road hazards. For example, processing unit 110 may estimatecamera motion between consecutive image frames and calculate thedisparities in pixels between the frames to construct a 3D-map of theroad. Processing unit 110 may then use the 3D-map to detect the roadsurface, as well as hazards existing above the road surface.

At step 530, processing unit 110 may execute navigational responsemodule 408 to cause one or more navigational responses in vehicle 200based on the analysis performed at step 520 and the techniques asdescribed above in connection wish FIG. 4. Navigational responses mayinclude, for example, a turn, a lane shift, a change in acceleration,and the like. In some embodiments, processing unit 110 may use dataderived from execution of velocity and acceleration module 406 to causethe one or more navigational responses. Additionally, multiplenavigational responses may occur simultaneously, in sequence, or anycombination thereof. For instance, processing unit 110 may cause vehicle200 to shift one lane over and then accelerate by, for example,sequentially transmitting control signals to steering system 240 andthrottling system 220 of vehicle 200. Alternatively, processing unit 110may cause vehicle 200 to brake while at the same time shifting lanes by,for example, simultaneously transmitting control signals to brakingsystem 230 and steering system 240 of vehicle 200.

FIG. 5B is a flowchart showing an exemplary process 500B for detectingone or more vehicles and/or pedestrians in a set of images, consistentwith disclosed embodiments. Processing unit 110 may execute monocularimage analysis module 402 to implement process 5008. At step 540,processing unit 110 may determine a set of candidate objectsrepresenting possible vehicles and/or pedestrians. For example,processing unit 110 may scan one or more images, compare the images toone or more predetermined patterns, and identify within each imagepossible locations that may contain objects of interest (e.g., vehicles,pedestrians, or portions thereof). The predetermined patterns may bedesigned in such a way to achieve a high rate of “false hits” and a lowrate of “misses.” For example, processing unit 110 to may use a lowthreshold of similarity to predetermined patterns for identifyingcandidate objects as possible vehicles or pedestrians. Doing so mayallow processing unit 110 to reduce the probability of missing (e.g.,not identifying) a candidate object representing a vehicle orpedestrian.

At step 542, processing unit 110 may filter the set of candidate objectsto exclude certain candidates (e.g., irrelevant or less relevantobjects) based on classification criteria. Such criteria may be derivedfrom various properties associated with object types stored in adatabase (e.g., a database stored in memory 140). Properties may includeobject shape, dimensions, texture, position (e.g., relative to vehicle200), and the like. Thus, processing unit 110 may use one or more setsof criteria to reject false candidates from the set of candidateobjects.

At step 544, processing unit 110 may analyze multiple frames of imagesto determine whether objects in the set of candidate objects representvehicles and/or pedestrians. For example, processing unit 110 may tracka detected candidate object across consecutive frames and accumulateframe-by-frame data associated with the detected object (e.g., size,position relative to vehicle 200, etc.) Additionally, processing unit110 may estimate parameters for the detected object and compare theobject's frame-by-frame position data to a predicted position.

At step 546, processing unit 110 may construct a set of measurements forthe detected objects. Such measurements may include, for example,position, velocity, and acceleration values (relative to vehicle 200)associated with the detected objects. In some embodiments, processingunit 110 may construct the measurements based on estimation techniquesusing a series of time-based observations such as Kalman filters orlinear quadratic estimation (LQE), and/or based on available modelingdata for different object types (e.g., cars, trucks, pedestrians,bicycles, road signs, etc.). The Kalman filters may be based on ameasurement of an object's scale, where the scale measurement isproportional to a time to collision (e.g., the amount of time forvehicle 200 to reach the object). Thus, by performing steps 540-546,processing unit 110 may identify vehicles and pedestrians appearingwithin the set of captured images and derive information (e.g.,position, speed, size) associated with the vehicles and pedestrians.Based on the identification and the derived information, processing unit110 may cause one or more navigational responses in vehicle 200, asdescribed in connection with FIG. 5A, above.

At step 548, processing unit 110 may perform an optical flow analysis ofone or more images to reduce the probabilities of detecting a “falsehit” and missing a candidate object that represents a vehicle orpedestrian. The optical flow analysis may refer to, for example,analyzing motion patterns relative to vehicle 200 in the one or moreimages associated with other vehicles and pedestrians, and that aredistinct from road surface motion. Processing unit 110 may calculate themotion of candidate objects by observing the different positions of theobjects across multiple image frames, which are captured at differenttimes. Processing unit 110 may use the position and time values asinputs into mathematical models for calculating the motion of thecandidate objects. Thus, optical flow analysis may provide anothermethod of detecting vehicles and pedestrians that are nearby vehicle200. Processing unit 110 may perform optical flow analysis incombination with steps 540-546 to provide redundancy for detectingvehicles and pedestrians and increase the reliability of system 100.

FIG. 5C is a flowchart showing an exemplary process 500C for detectingroad marks and/or lane geometry information in a set of images,consistent with disclosed embodiments. Processing unit 110 may executemonocular image analysis module 402 to implement process 500C. At step550, processing unit 110 may detect a set of objects by scanning one ormore images. To detect segments of lane markings, lane geometryinformation, and other pertinent road marks, processing unit 110 mayfilter the set of objects to exclude those determined to be irrelevant(e.g., minor potholes, small rocks, etc.). At step 552, processing unit110 may group together the segments detected in step 550 belonging tothe same road mark or lane mark. Based on the grouping, processing unit110 may develop a model to represent the detected segments, such as amathematical model.

At step 554, processing unit 110 may construct a set of measurementsassociated with the detected segments. In some embodiments, processingunit 110 may create a projection of the detected segments from the imageplane onto the real-world plane. The projection may be characterizedusing a 3rd-degree polynomial having coefficients corresponding tophysical properties such as the position, slope, curvature, andcurvature derivative of the detected road. In generating the projection,processing unit 110 may take into account changes in the road surface,as well as pitch and roll rates associated with vehicle 200. Inaddition, processing unit 110 may model the road elevation by analyzingposition and motion cues present on the road surface. Further,processing unit 110 may estimate the pitch and roll rates associatedwith vehicle 200 by tracking a set of feature points in the one or moreimages.

At step 556, processing unit 110 may perform multi-frame analysis by,for example, tracking the detected segments across consecutive imageframes and accumulating frame-by-frame data associated with detectedsegments. As processing unit 110 performs multi-frame analysis, the setof measurements constructed at step 554 may become more reliable andassociated with an increasingly higher confidence level. Thus, byperforming steps 550-556, processing unit 110 may identify road marksappearing within the set of captured images and derive lane geometryinformation. Based on the identification and the derived information,processing unit 110 may cause one or more navigational responses invehicle 200, as described in connection with FIG. 5A, above.

At step 558, processing unit 110 may consider additional sources ofinformation to further develop a safety model for vehicle 200 in thecontext of its surroundings. Processing unit 110 may use the safetymodel to define a context in which system 100 may execute autonomouscontrol of vehicle 200 in a safe manner. To develop the safety model, insome embodiments, processing unit 110 may consider the position andmotion of other vehicles, the detected road edges and barriers, and/orgeneral road shape descriptions extracted from map data (such as datafrom map database 160). By considering additional sources ofinformation, processing unit 110 may provide redundancy for detectingroad marks and lane geometry and increase the reliability of system 100.

FIG. 5D is a flowchart showing an exemplary process 500D for detectingtraffic lights in a set of images, consistent with disclosedembodiments. Processing unit 110 may execute monocular image analysismodule 402 to implement process 500D. At step 560, processing unit 110may scan the set of images and identify objects appearing at locationsin the images likely to contain traffic lights. For example, processingunit 110 may filter the identified objects to construct a set ofcandidate objects, excluding those objects unlikely to correspond totraffic lights. The filtering may be done based on various propertiesassociated with traffic lights, such as shape, dimensions, texture,position (e.g., relative to vehicle 200), and the like. Such propertiesmay be based on multiple examples of traffic lights and traffic controlsignals and stored in a database. In some embodiments, processing unit110 may perform multi-frame analysis on the set of candidate objectsreflecting possible traffic lights. For example, processing unit 110 maytrack the candidate objects across consecutive image frames, estimatethe real-world position of the candidate objects, and filter out thoseobjects that are moving (which are unlikely to be traffic lights). Insome embodiments, processing unit 110 may perform color analysis on thecandidate objects and identify the relative position of the detectedcolors appearing inside possible traffic lights.

At step 562, processing unit 110 may analyze the geometry of a junction.The analysis may be based on any combination of: (i) the number of lanesdetected on either side of vehicle 200, (ii) markings (such as arrowmarks) detected on the road, and (iii) descriptions of the junctionextracted from map data (such as data from map database 160). Processingunit 110 may conduct the analysis using information derived fromexecution of monocular analysis module 402. In addition, Processing unit110 may determine a correspondence between the traffic lights detectedat step 560 and the lanes appearing near vehicle 200.

As vehicle 200 approaches the junction, at step 564, processing unit HOmay update the confidence level associated with the analyzed junctiongeometry and the detected traffic lights. For instance, the number oftraffic lights estimated to appear at the junction as compared with thenumber actually appearing at the junction may impact the confidencelevel. Thus, based on the confidence level, processing unit 110 maydelegate control to the driver of vehicle 200 in order to improve safetyconditions. By performing steps 560-564, processing unit 110 mayidentify traffic lights appearing within the set of captured images andanalyze junction geometry information. Based on the identification andthe analysis, processing unit 110 may cause one or more navigationalresponses in vehicle 200, as described in connection with FIG. 5A,above.

FIG. 5E is a flowchart showing an exemplary process 500E for causing oneor more navigational responses in vehicle 200 based on a vehicle path,consistent with the disclosed embodiments. At step 570, processing unit110 may construct an initial vehicle path associated with vehicle 200.The vehicle path may be represented using a set of points expressed incoordinates (x, z), and the distance d_(i) between two points in the setof points may fall in the range of 1 to 5 meters. In one embodiment,processing unit 110 may construct the initial vehicle path using twopolynomials, such as left and right road polynomials. Processing unit110 may calculate the geometric midpoint between the two polynomials andoffset each point included in the resultant vehicle path by apredetermined offset (e.g., a smart lane offset), if any (an offset ofzero may correspond to travel in the middle of a lane). The offset maybe in a direction perpendicular to a segment between any two points inthe vehicle path. In another embodiment, processing unit 110 may use onepolynomial and an estimated lane width to offset each point of thevehicle path by half the estimated lane width plus a predeterminedoffset (e.g., a smart lane offset).

At step 572, processing unit 110 may update the vehicle path constructedat step 570. Processing unit 110 may reconstruct the vehicle pathconstructed at step 570 using a higher resolution, such that thedistance d_(k) between two points in the set of points representing thevehicle path is less than the distance d_(i) described above. Forexample, the distance d_(k) may fall in the range of 0.1 to 0.3 meters.Processing unit 110 may reconstruct the vehicle path using a parabolicspline algorithm, which may yield a cumulative distance vector Scorresponding to the total length of the vehicle path (i.e., based onthe set of points representing the vehicle path).

At step 574, processing unit 110 may determine a look-ahead point(expressed in coordinates as (x_(i), z_(t))) based on the updatedvehicle path constructed at step 572. Processing unit 110 may extractthe look-ahead point from the cumulative distance vector S, and thelook-ahead point may be associated with a look-ahead distance andlook-ahead time. The look-ahead distance, which may have a lower boundranging from 10 to 20 meters, may be calculated as the product of thespeed of vehicle 200 and the look-ahead time. For example, as the speedof vehicle 200 decreases, the look-ahead distance may also decrease(e.g., until it reaches the lower bound). The look-ahead time, which mayrange from 0.5 to 1.5 seconds, may be inversely proportional to the gainof one or more control loops associated with causing a navigationalresponse in vehicle 200, such as the heading error tracking controlloop. For example, the gain of the heading error tracking control loopmay depend on the bandwidth of a yaw rate loop, a steering actuatorloop, car lateral dynamics, and the like. Thus, the higher the gain ofthe heading error tracking control loop, the lower the look-ahead time.

At step 576, processing unit 110 may determine a heading error and yawrate command based on the look-ahead point determined at step 574.Processing unit 110 may determine the heading error by calculating thearctangent of the look-ahead point, e.g., arctan (x_(l)/z_(t)).Processing unit 110 may determine the yaw rate command as the product ofthe heading error and a high-level control gain. The high-level controlgain may be equal to: (2/look-ahead time), if the look-ahead distance isnot at the lower bound. Otherwise, the high-level control gain may beequal to: (2*speed of vehicle 200/look-ahead distance).

FIG. 5F is a flowchart showing an exemplary process 500F for determiningwhether a leading vehicle is changing lanes, consistent with thedisclosed embodiments. At step 580, processing unit 110 may determinenavigation information associated with a leading vehicle (e.g., avehicle traveling ahead of vehicle 200). For example, processing unit110 may determine the position, velocity (e.g., direction and speed),and/or acceleration of the leading vehicle, using the techniquesdescribed in connection with FIGS. 5A and 5B, above. Processing unit 110may also determine one or more road polynomials, a look-ahead point(associated with vehicle 200), and/or a snail trail (e.g., a set ofpoints describing a path taken by the leading vehicle), using thetechniques described in connection with FIG. 5E, above.

At step 582, processing unit 110 may analyze the navigation informationdetermined at step 580. In one embodiment, processing unit 110 maycalculate the distance between a snail trail and a road polynomial(e.g., along the trail). If the variance of this distance along thetrail exceeds a predetermined threshold (for example, 0.1 to 0.2 meterson a straight road, 0.3 to 0.4 meters on a moderately curvy road, and0.5 to 0.6 meters on a road with sharp curves), processing unit 110 maydetermine that the leading vehicle is likely changing lanes. In the casewhere multiple vehicles are detected traveling ahead of vehicle 200,processing unit 110 may compare the snail trails associated with eachvehicle. Based on the comparison, processing unit 110 may determine thata vehicle whose snail trail does not match with the snail trails of theother vehicles is likely changing lanes. Processing unit HO mayadditionally compare the curvature of the snail trail (associated withthe leading vehicle) with the expected curvature of the road segment inwhich the leading vehicle is traveling. The expected curvature may beextracted from map data (e.g., data from map database 160), from roadpolynomials, from other vehicles' snail trails, from prior knowledgeabout the road, and the like. If the difference in curvature of thesnail trail and the expected curvature of the road segment exceeds apredetermined threshold, processing unit 110 may determine that theleading vehicle is likely changing lanes.

In another embodiment, processing unit 110 may compare the leadingvehicle's instantaneous position with the look-ahead point (associatedwith vehicle 200) over a specific period of time (e.g., 0.5 to 1.5seconds). If the distance between the leading vehicle's instantaneousposition and the look-ahead point varies during the specific period oftime, and the cumulative sum of variation exceeds a predeterminedthreshold (for example, 0.3 to 0.4 meters on a straight road, 0.7 to 0.8meters on a moderately curvy road, and 1.3 to 1.7 meters on a road withsharp curves), processing unit 110 may determine that the leadingvehicle is likely changing lanes. In another embodiment, processing unit110 may analyze the geometry of the snail trail by comparing the lateraldistance traveled along the trail with the expected curvature of thesnail trail. The expected radius of curvature may be determinedaccording to the calculation: (δ_(z) ²+δ_(x) ²)/2/(δ_(x)), where δ_(x)represents the lateral distance traveled and δ_(z) represents thelongitudinal distance traveled. If the difference between the lateraldistance traveled and the expected curvature exceeds a predeterminedthreshold (e.g., 500 to 700 meters), processing unit 110 may determinethat the leading vehicle is likely changing lanes. In anotherembodiment, processing unit 110 may analyze the position of the leadingvehicle. If the position of the leading vehicle obscures a roadpolynomial (e.g., the leading vehicle is overlaid on top of the roadpolynomial), then processing unit 110 may determine that the leadingvehicle is likely changing lanes. In the case where the position of theleading vehicle is such that, another vehicle is detected ahead of theleading vehicle and the snail trails of the two vehicles are notparallel, processing unit 110 may determine that the (closer) leadingvehicle is likely changing lanes.

At step 584, processing unit 110 may determine whether or not leadingvehicle 200 is changing lanes based on the analysis performed at step582. For example, processing unit 110 may make the determination basedon a weighted average of the individual analyses performed at step 582.Under such a scheme, for example, a decision by processing unit 110 thatthe leading vehicle is likely changing lanes based on a particular typeof analysis may be assigned a value of “1” (and “0” to represent adetermination that the leading vehicle is not likely changing lanes).Different analyses performed at step 582 may be assigned differentweights, and the disclosed embodiments are not limited to any particularcombination of analyses and weights. Furthermore, in some embodiments,the analysis may make use of trained system (e.g., a machine learning ordeep learning system), which may, for example, estimate a future pathahead of a current location of a vehicle based on an image captured atthe current location.

FIG. 6 is a flowchart showing an exemplary process 600 for causing oneor more navigational responses based on stereo image analysis,consistent with disclosed embodiments. At step 610, processing unit 110may receive a first and second plurality of images via data interface128. For example, cameras included in image acquisition unit 120 (suchas image capture devices 122 and 124 having fields of view 202 and 204)may capture a first and second plurality of images of an area forward ofvehicle 200 and transmit them over a digital connection (e.g., USB,wireless, Bluetooth, etc.) to processing unit 110. In some embodiments,processing unit 110 may receive the first and second plurality of imagesvia two or more data interfaces. The disclosed embodiments are notlimited to any particular data interface configurations or protocols.

At step 620, processing unit 110 may execute stereo image analysismodule 404 to perform stereo image analysis of the first and secondplurality of images to create a 3D map of the road in front of thevehicle and detect features within the images; such as lane markings,vehicles, pedestrians, road signs, highway exit ramps, traffic lights,road hazards, and the like. Stereo image analysis may be performed in amanner similar to the steps described in connection with FIGS. 5A-5D,above. For example, processing unit 110 may execute stereo imageanalysis module 404 to detect candidate objects (e.g., vehicles,pedestrians, road marks, traffic light, road hazards, etc.) within thefirst and second plurality of images, filter out a subset of thecandidate objects based on various criteria, and perform multi-frameanalysis, construct measurements, and determine a confidence level forthe remaining candidate objects. In performing the steps above,processing unit 110 may consider information from both the first andsecond plurality of images, rather than information from one set ofimages alone. For example, processing unit 110 may analyze thedifferences in pixel-level data (or other data subsets from among thetwo streams of captured images) for a candidate object appearing in boththe first and second plurality of images. As another example, processingunit 110 may estimate a position and/or velocity of a candidate object(e.g., relative to vehicle 200) by observing that the object appears inone of the plurality of images but not the other or relative to otherdifferences that may exist relative to objects appearing in the twoimage streams. For example, position, velocity, and/or accelerationrelative to vehicle 200 may be determined based on trajectories,positions, movement characteristics, etc. of Features associated with anobject appearing in one or both of the image streams.

At step 630, processing unit 110 may execute navigational responsemodule 408 to cause one or more navigational responses in vehicle 200based on the analysis performed at step 620 and the techniques asdescribed above in connection with FIG. 4. Navigational responses mayinclude, for example, a turn, a lane shift, a change in acceleration, achange in velocity, braking, and the like. In some embodiments,processing unit 110 may use data derived from execution of velocity andacceleration module 406 to cause the one or more navigational responses.Additionally, multiple navigational responses may occur simultaneously,in sequence, or any combination thereof.

FIG. 7 is a flowchart showing an exemplary process 700 for causing oneor more navigational responses based on an analysis of three sets ofimages, consistent with disclosed embodiments. At step 710, processingunit 110 may receive a first, second, and third plurality of images viadata interface 128. For instance, cameras included in image acquisitionunit 120 (such as image capture devices 122, 124, and 126 having fieldsof view 202, 204, and 206) may capture a first, second, and thirdplurality of images of an area forward and/or to the side of vehicle 200and transmit them over a digital connection (e.g., USB, wireless,Bluetooth, etc.) to processing unit 110. In some embodiments, processingunit 110 may receive the first, second, and third plurality of imagesvia three or more data interfaces. For example, each of image capturedevices 122, 124, 126 may have an associated data interface forcommunicating data to processing unit 110. The disclosed embodiments arenot limited to any particular data interface configurations orprotocols.

At step 720, processing unit 110 may analyze the first, second, andthird plurality of images to detect features within the images, such aslane markings, vehicles, pedestrians, road signs, highway exit ramps,traffic lights, road hazards, and the like. The analysis may beperformed in a manner similar to the steps described in connection withFIGS. 5A-5D and 6, above. For instance, processing unit 110 may performmonocular image analysis (e.g., via execution of monocular imageanalysis module 402 and based on the steps described in connection withFIGS. 5A-5D, above) on each of the first, second, and third plurality ofimages. Alternatively, processing unit 110 may perform stereo imageanalysis (e.g., via execution of stereo image analysis module 404 andbased on the steps described in connection with FIG. 6, above) on thefirst and second plurality of images, the second and third plurality ofimages, and/or the first and third plurality of images. The processedinformation corresponding to the analysis of the first, second, and/orthird plurality of images may be combined. In some embodiments,processing unit 110 may perform a combination of monocular and stereoimage analyses. For example, processing unit 110 may perform monocularimage analysis (e.g., via execution of monocular image analysis module402) on the first plurality of images and stereo image analysis (e.g.,via execution of stereo image analysis module 404) on the second andthird plurality of images. The configuration of image capture devices122, 124, and 126—including their respective locations and fields ofview 202, 204, and 206—may influence the types of analyses conducted onthe first, second, and third plurality of images. The disclosedembodiments are not limited to a particular configuration of imagecapture devices 122, 124, and 126, or the types of analyses conducted onthe first, second, and third plurality of images.

In some embodiments, processing unit 110 may perform testing on system100 based on the images acquired and analyzed at steps 710 and 720. Suchtesting may provide an indicator of the overall performance of system100 for certain configurations of image capture devices 122, 124, and126. For example, processing unit 110 may determine the proportionof“false hits” (e.g., cases where system 100 incorrectly determined thepresence of a vehicle or pedestrian) and “misses.”

At step 730, processing unit 110 may cause one or more navigationalresponses in vehicle 200 based on information derived from two of thefirst, second, and third plurality of images. Selection of two of thefirst, second, and third plurality of images may depend on variousfactors, such as, for example, the number, types, and sizes of objectsdetected in each of the plurality of images. Processing unit 110 mayalso make the selection based on image quality and resolution, theeffective field of view reflected in the images, the number of capturedframes, the extent to which one or more objects of interest actuallyappear in the frames (e.g., the percentage of frames in which an objectappears. the proportion of the object that appears in each such frame,etc.), and the like.

In some embodiments, processing unit 110 may select information derivedfrom two of the first, second, and third plurality of images bydetermining the extent to which information derived from one imagesource is consistent with information derived from other image sources.For example, processing unit 110 may combine the processed informationderived from each of image capture devices 122, 124, and 126 (whether bymonocular analysis, stereo analysis, or any combination of the two) anddetermine visual indicators (e.g., lane markings, a detected vehicle andits location and/or path, a detected traffic light, etc.) that areconsistent across the images captured from each of image capture devices122, 124, and 126. Processing unit 110 may also exclude information thatis inconsistent across the captured images (e.g., a vehicle changinglanes, a lane model indicating a vehicle that is too close to vehicle200, etc.). Thus, processing unit 110 may select information derivedfrom two of the first, second, and third plurality of images based onthe determinations of consistent and inconsistent information.

Navigational responses may include, for example, a turn, a lane shift, achange in acceleration, and the like. Processing unit 110 may cause theone or more navigational responses based on the analysis performed atstep 720 and the techniques as described above in connection with FIG.4. Processing unit 110 may also use data derived from execution ofvelocity and acceleration module 406 to cause the one or morenavigational responses. In some embodiments, processing unit 110 maycause the one or more navigational responses based on a relativeposition, relative velocity, and/or relative acceleration betweenvehicle 200 and an object detected within any of the first, second, andthird plurality of images. Multiple navigational responses may occursimultaneously, in sequence, or any combination thereof.

Reinforcement Learning and Trained Navigational Systems

The sections that follow discuss autonomous driving along with systemsand methods for accomplishing autonomous control of a vehicle, whetherthat control is fully autonomous (a self-driving vehicle) or partiallyautonomous (e.g., one or more driver assist systems or functions). Asshown in FIG. 8, the autonomous driving task can be partitioned intothree main modules, including a sensing module 801, a driving policymodule 803, and a control module 805. In some embodiments, modules 801,803, and 805 may be stored in memory unit 140 and/or memory unit 150 ofsystem 100, or modules 801, 803, and 805 (or portions thereof) may bestored remotely from system 100 (e.g., stored in a server accessible tosystem 100 via, for example, wireless transceiver 172). Furthermore, anyof the modules (e.g., modules 801, 803, and 805) disclosed herein mayimplement techniques associated with a trained system (such as a neuralnetwork or a deep neural network) or an untrained system.

Sensing module 801, which may be implemented using processing unit 110,may handle various tasks relating to sensing of a navigational state inan environment of a host vehicle. Such tasks may rely upon input fromvarious sensors and sensing systems associated with the host vehicle.These inputs may include images or image streams from one or moreonboard cameras, GPS position information, accelerometer outputs, userfeedback, or user inputs to one or more user interface devices, radar,lidar, etc. Sensing, which may include data from cameras and/or anyother available sensors, along with map information, may be collected,analyzed, and formulated into a “sensed state,” describing informationextracted from a scene in the environment of the host vehicle. Thesensed state may include: sensed information relating to targetvehicles, lane markings, pedestrians, traffic lights, road geometry,lane shape, obstacles, distances to other objects/vehicles, relativevelocities, relative accelerations, among any other potential sensedinformation. Supervised machine learning may be implemented in order toproduce a sensing state output based on sensed data provided to sensingmodule 801. The output of the sensing module may represent a sensednavigational “state” of the host vehicle, which may be passed to drivingpolicy module 803.

While a sensed state may be developed based on image data received fromone or more cameras or image sensors associated with a host vehicle, asensed state for use in navigation may be developed using any suitablesensor or combination of sensors. In some embodiments, the sensed statemay be developed without reliance upon captured image data. In fact, anyof the navigational principles described herein may be applicable tosensed states developed based on captured image data as well as sensedstates developed using other non-image based sensors. The sensed statemay also be determined via sources external to the host vehicle. Forexample, a sensed state may be developed in full or in part based oninformation received from sources remote from the host vehicle (e.g.,based on sensor information, processed state information, etc. sharedfrom other vehicles, shared from a central server, or from any othersource of information relevant to a navigational state of the hostvehicle.)

Driving policy module 803, which is discussed in more detail below andwhich may be implemented using processing unit 110, may implement adesired driving policy in order to decide on one or more navigationalactions for the host vehicle to take in response to the sensednavigational state. If there are no other agents (e.g., target vehiclesor pedestrians) present in the environment of the host vehicle, thesensed state input to driving policy module 803 may be handled in arelatively straightforward manner. The task becomes more complex whenthe sensed state requires negotiation with one or more other agents. Thetechnology used to generate the output of driving policy module 803 mayinclude reinforcement learning (discussed in more detail below). Theoutput of driving policy module 803 may include at least onenavigational action for the host vehicle and may include a desiredacceleration (which may translate to an updated speed for the hostvehicle), a desired yaw rate for the host vehicle, a desired trajectory,among other potential desired navigational actions.

Based on the output from the driving policy module 803, control module805, which may also be implemented using processing unit 110, maydevelop control instructions for one or more actuators or controlleddevices associated with the host vehicle. Such actuators and devices mayinclude an accelerator, one or more steering controls, a brake, a signaltransmitter, a display, or any other actuator or device that may becontrolled as part of a navigation operation associated with a hostvehicle. Aspects of control theory may be used to generate the output ofcontrol module 805. Control module 805 may be responsible for developingand outputting instructions to controllable components of the hostvehicle in order to implement the desired navigational goals orrequirements of driving policy module 803.

Returning to driving policy module 803, in some embodiments, a trainedsystem trained through reinforcement learning may be used to implementdriving policy module 803. In other embodiments, driving policy module803 may be implemented without a machine learning approach, by usingspecified algorithms to “manually” address the various scenarios thatmay arise during autonomous navigation. Such an approach, however, whileviable, may result in a driving policy that is too simplistic and maylack the flexibility of a trained system based on machine learning. Atrained system, for example, may be better equipped to handle complexnavigational states and may better determine whether a taxi is parkingor is stopping to pick up or drop off a passenger; determine whether apedestrian intends to cross the street ahead of the host vehicle;balance unexpected behavior of other drivers with defensiveness;negotiate in dense traffic involving target vehicles and/or pedestrians;decide when to suspend certain navigational rules or augment otherrules; anticipate unsensed, but anticipated conditions (e.g., whether apedestrian will emerge from behind a car or obstacle); etc. A trainedsystem based on reinforcement learning may also be better equipped toaddress a state space that is continuous and high-dimensional along withan action space that is continuous.

Training of the system using reinforcement learning may involve learninga driving policy in order to map from sensed states to navigationalactions. A driving policy is a function π: S→A, where S is a set ofstates and A⊂

² is the action space (e.g., desired speed, acceleration, yaw commands,etc.). The state space is S=S_(s)×S_(p), where S_(p) is the sensingstate and S_(p) is additional information on the state saved by thepolicy. Working in discrete time intervals, at time t, the current states_(t)∈S may be observed, and the policy may be applied to obtain adesired action, α_(t)=π(s_(t)).

The system may be trained through exposure to various navigationalstates, having the system apply the policy, providing a reward (based ona reward function designed to reward desirable navigational behavior).Based on the reward feedback, the system may “learn” the policy andbecomes trained in producing desirable navigational actions. Forexample, the learning system may observe the current state s_(t)∈S anddecide on an action α_(t)∈A based on a policy π: S→

(A). Based on the decided action (and implementation of the action theenvironment moves to the next state s_(t+1)∈S for observation by thelearning system. For each action developed in response to the observedstate, the feedback to the learning system is a reward signal r₁, r₂, .. . .

The goal of Reinforcement Learning (RL) is to find a policy π. It isusually assumed that at time t, there is a reward function r_(t), whichmeasures the instantaneous quality of being at state s, and takingaction a_(t). However, taking the action a_(t) at time t affects theenvironment and therefore affects the value of the future states. As aresult, when deciding on what action to take, not only should thecurrent reward be taken into account, but future rewards should also beconsidered. In some instances the system should take a certain action,even though it is associated with a reward lower than another availableoption, when the system determines that in the future a greater rewardmay be realized if the lower reward option is taken now. To formalizethis, observe that a policy, π, and an initial state, s, induces adistribution over

^(T), where the probability of a vector (r₁, . . . , r_(T)) is theprobability of observing the rewards r_(i), . . . , r_(T), if the agentstarts at state s₀=s and from there on follows the policy κ. The valueof the initial state s may be defined as:

${V^{\pi}(s)} = {{\left\lbrack {{\left. {\sum\limits_{t = 1}^{T}r_{t}} \middle| s_{0} \right. = s},{\forall{t \geq 1}},{a_{t} = {\pi \left( s_{t} \right)}}} \right\rbrack}.}$

Instead of restricting the time horizon to T, the future rewards may bediscounted to define, for some fixed γ∈(0, 1):

${V^{\pi}(s)} = {{\left\lbrack {{\left. {\sum\limits_{t = 1}^{\infty}{\gamma^{t}r_{t}}} \middle| s_{0} \right. = s},{\forall{t \geq 1}},{a_{t} = {\pi \left( s_{t} \right)}}} \right\rbrack}.}$

In any case, the optimal policy is the solution of

$\underset{\pi}{argmax}\mspace{14mu} {\left\lbrack {V^{\pi}(s)} \right\rbrack}$

where the expectation is over the initial state, s.

There are several possible methodologies for training the driving policysystem. For example, an imitation approach (e.g., behavior cloning) maybe used in which the system learns from state/action pairs where theactions are those that would be chosen by a good agent a human) inresponse to a particular observed state. Suppose a human driver isobserved. Through this observation, many examples of the form (s_(i),a_(t)), where s, is the state and a_(t) is the action of the humandriver could be obtained, observed, and used as a basis for training thedriving policy system. For example, supervised learning can be used tolearn a policy π such that π(s_(t))≈a_(t). There are many potentialadvantages of this approach. First, there is no requirement to define areward function. Second, the learning is supervised and happens offline(there is no need to apply the agent in the learning process). Adisadvantage of this method is that different human drivers, and eventhe same human drivers, are not deterministic in their policy choices.Hence, learning a function for which ∥π(s_(t))−a_(t)∥ is very small isoften infeasible. And, even small errors may accumulate over time toyield large errors.

Another technique that may be employed is policy based learning. Here,the policy may be expressed in parametric form and directly optimizedusing a suitable optimization technique (e.g., stochastic gradientdescent). The approach is to directly solve the problem given in

$\underset{\pi}{argmax}\mspace{14mu} {{\left\lbrack {V^{\pi}(s)} \right\rbrack}.}$

There are of course many ways to solve the problem. One advantage ofthis approach is that it tackles the problem directly, and thereforeoften leads to good practical results. One potential disadvantage isthat it often requires an “on-policy” training, namely, the learning ofπ is an iterative process, where at iteration j we have a non-perfectpolicy, π_(j), and to construct the next policy π_(j), we must interactwith the environment while acting based on π_(j).

The system may also be trained through value based learning (learning Qor V functions). Suppose a good approximation can be learned to theoptimal value function V*. An optimal policy may be constructed (e.g.,by relying on the Bellman equation). Some versions of value basedlearning can be implemented offline (called “off-policy” training). Somedisadvantages of the value-based approach may result from its strongdependence on Markovian assumptions and required approximation of acomplicated function (it may be more difficult to approximate the valuefunction than to approximate the policy directly).

Another technique may include model based learning and planning(learning probability of state transitions and solving the optimizationproblem of finding the optimal V). Combinations of these techniques mayalso be used to train the learning system. In this approach, thedynamics of the process may be learned, namely, the function that takes(s_(i), a_(t)) and yields a distribution over the next state s_(t+1).Once this function is learned, the optimization problem may be solved tofind the policy IC whose value is optimal. This is called “planning”.One advantage of this approach may be that the learning part issupervised and can be applied offline by observing triplets (s_(t),a_(t), s_(t+1)). One disadvantage of this approach, similar to the“imitation” approach, may be that small errors in the learning processcan accumulate and to yield inadequately performing policies.

Another approach for training driving policy module 803 may includedecomposing the driving policy function into semantically meaningfulcomponents. This allows implementation of parts of the policy manually,which may ensure the safety of the policy, and implementation of otherparts of the policy using reinforcement learning techniques, which mayenable adaptivity to many scenarios, a human-like balance betweendefensive/aggressive behavior, and a human-like negotiation with otherdrivers. From the technical perspective, a reinforcement learningapproach may combine several methodologies and offer a tractabletraining procedure, where most of the training can be performed usingeither recorded data or a self-constructed simulator.

In some embodiments, training of driving policy module 803 may rely uponan “options” mechanism. To illustrate, consider a simple scenario of adriving policy for a two-lane highway. In a direct RL approach, a policyat that maps the state into A⊂

², where the first component of a (s) is the desired accelerationcommand and the second component of (s) is the yaw rate. In a modifiedapproach, the following policies can be constructed:

Automatic Cruise Control (ACC) policy, o_(ACC): S→A: this policy alwaysoutputs a yaw rate of 0 and only changes the speed so as to implementsmooth and accident-free driving.

ACC+Left+policy, o_(L): S→A: the longitudinal command of this policy isthe same as the ACC command. The yaw rate is a straightforwardimplementation of centering the vehicle toward the middle of the leftlane, while ensuring a safe lateral movement (e.g., don't move left ifthere's a car on the left side).

ACC+Right policy, o_(R): S→A: Same as o_(L), but the vehicle may becentered toward the middle of the right lane.

These policies may be referred to as “options”. Relying on these“options”, a policy can be learned that selects options, π_(o): S→O,where O is the set of available options. In one case, O={o_(ACC), o_(L),o_(R)}. The option-selector policy, π_(o), defines an actual policy, π:S→A, by setting, for every s, π(s)=o_(π) _(o) _((s))(s).

In practice, the policy function may be decomposed into an options graph901, as shown in FIG. 9. Another example options graph 1000 is shown inFIG. 10. The options graph can represent a hierarchical set of decisionsorganized as a Directed Acyclic Graph (DAG). There is a special nodecalled the root node 903 of the graph. This node has no incoming nodes.The decision process traverses through the graph, starting from the rootrode, until it reaches a “leaf” node, which refers to a node that has nooutgoing decision lines. As shown in FIG. 9, leaf nodes may includenodes 905, 907, and 909, for example. Upon encountering a leaf node,driving policy module 803 may output the acceleration and steeringcommands associated with a desired navigational action associated withthe leaf node.

Internal nodes, such as nodes 911, 913, and 915, for example, may resultin implementation of a policy that chooses a child among its availableoptions. The set of available children of an internal node include allof the nodes associated with a particular internal node via decisionlines. For example, internal node 913 designated as “Merge” in FIG. 9includes three children nodes 909, 915, and 917 (“Stay,” “OvertakeRight,” and “Overtake Left,” respectively) each joined to node 913 by adecision line.

Flexibility of the decision-making system may be gained by enablingnodes to adjust their position in the hierarchy of the options graph.For example, any of the nodes may be allowed to declare themselves as“critical.” Each node may implement a function “is critical,” thatoutputs “True” if the node is in a critical section of its policyimplementation. For example, a node that is responsible for a take-over,may declare itself as critical while in the middle of a maneuver. Thismay impose constraints on the set of available children of a node u,which may include all nodes v which are children of node u and for whichthere exists a path from v to a leaf node that goes through all nodesdesignated as critical. Such an approach may allow, on one hand,declaration of the desired path on the graph at each time step, while onthe other hand, stability of a policy may be preserved, especially whilecritical portions of the policy are being implemented.

By defining an options graph, the problem of learning the driving policyit: S→A may be decomposed into a problem of defining a policy for eachnode of the graph, where the policy at internal nodes should choose fromamong available children nodes. For some of the nodes, the respectivepolicy may be implemented manually (e.g., through if-then typealgorithms specifying a set of actions in response to an observed state)while for others the policies may be implemented using a trained systembuilt through reinforcement learning. The choice between manual ortrained/learned approaches may depend on safety aspects associated withthe task and on its relative simplicity. The option graphs may beconstructed in a manner such that some of the nodes are straightforwardto implement, while other nodes may rely on trained models. Such anapproach can ensure safe operation of the system.

The following discussion provides further details regarding the role ofthe options graph of FIG. 9 within driving policy module 803. Asdiscussed above, the input to the driving policy module is a “sensedstate,” which summarizes the environment map, for example, as obtainedfrom available sensors. The output of driving policy module 803 is a setof desires (optionally, together with a set of hard constraints) thatdefine a trajectory as a solution of an optimization problem.

As described above, the options graph represents a hierarchical set ofdecisions organized as a DAG. There is a special node called the “root”of the graph. The root node is the only node that has no incoming edges(e.g., decision lines). The decision process traverses the graph,starting from the root node, until it reaches a “leaf” node, namely, anode that has no outgoing edges. Each internal node should implement apolicy that picks a child among its available children. Every leaf nodeshould implement a policy that, based on the entire path from the rootto the leaf, defines a set of Desires (e.g., a set of navigational goalsfor the host vehicle). The set of Desire-s, together with a set of hardconstraints that are defined directly based on the sensed state,establish an optimization problem whose solution is the trajectory forthe vehicle. The hard constraints may be employed to farther increasethe safety of the system, and the Desires can be used to provide drivingcomfort and human-like driving behavior of the system. The trajectoryprovided as a solution to the optimization problem, in turn, defines thecommands that should be provided to the steering, braking, and/or engineactuators in order to accomplish the trajectory.

Returning to FIG. 9, options graph 901 represents an options graph for atwo-lane highway, including with merging lanes (meaning that at somepoints, a third lane is merged into either the right or the left lane ofthe highway). The root node 903 first decides if the host vehicle is ina plain road scenario or approaching a merge scenario. This is anexample of a decision that can be implemented based on the sensingstate. Plain road node 911 includes three child nodes: stay node 909,overtake left node 917, and overtake right node 915. Stay refers to asituation in which the host vehicle would like to keep driving in thesame lane. The stay node is a leaf node (no outgoing edges/lines).Therefore, it the stay node defines a set of Desires. The first Desireit defines may include the desired lateral position e.g., as close aspossible to the center of the current lane of travel. There may also bea desire to navigate smoothly (e.g., within predefined or allowableacceleration maximums). The stay node may also define how the hostvehicle is to react to other vehicles. For example, the stay node mayreview sensed target vehicles and assign each a semantic meaning, whichcan be translated into components of the trajectory.

Various semantic meanings may be assigned to target vehicles in anenvironment of the host vehicle. For example, in some embodiments thesemantic meaning may include any of the following designations: 1) notrelevant: indicating that the sensed vehicle in the scene is currentlynot relevant; 2) next lane: indicating that the sensed vehicle is in anadjacent lane and an appropriate offset should be maintained relative tothis vehicle (the exact offset may be calculated in the optimizationproblem that constructs the trajectory given the Desires and hardconstraints, and can potentially be vehicle dependent—the stay leaf ofthe options graph sets the target vehicle's semantic type, which definesthe Desire relative to the target vehicle); 3) give way: the hostvehicle will attempt to give way to the sensed target vehicle by, farexample, reducing speed (especially where the host vehicle determinesthat the target vehicle is likely to cut into the lane of the hostvehicle); 4) take way: the host vehicle will attempt to take the rightof way by, for example, increasing speed; 5) follow: the host vehicledesires to maintain smooth driving following after this target vehicle;6) takeover left/right: this means the host vehicle would like toinitiate a lane change to the left or right lane. Overtake left node 917and overtake right node 915 are internal nodes that do not yet defineDesires.

The next node in options graph 901 is the select gap node 919. This nodemay be responsible for selecting a gap between two target vehicles in aparticular target lane that host vehicle desires to enter. By choosing anode of the form IDj, for some value of j, the host vehicle arrives at aleaf that designates a Desire for the trajectory optimizationproblem—e.g., the host vehicle wishes to make a maneuver so as to arriveat the selected gap. Such a maneuver may involve firstaccelerating/braking in the current lane and then heading to the targetlane at an appropriate time to enter the selected gap. If the select gapnode 919 cannot find an appropriate gap, it moves to the abort node 921,which defines a desire to move back to the center of the current laneand cancel the takeover.

Returning to merge node 913, when the host vehicle approaches a merge,it has several options that may depend on a particular situation. Forexample, as shown in FIG. 11A, host vehicle 1105 is traveling along atwo-lane road with no other target vehicles detected, either in theprimary lanes of the two-lane road or in the merge lane 1111. In thissituation, driving policy module 803, upon reaching merge node 913, mayselect stay node 909. That is, staying within its current lane may bedesired where no target vehicles are sensed as merging onto the roadway.

In FIG. 11B, the situation is slightly different. Here, host vehicle1105 senses one or more target vehicles 1107 entering the main roadway1112 from merge lane 1111. In this situation, once driving policy module803 encounters merge node 913, it may choose to initiate an overtakeleft maneuver in order to avoid the merging situation.

In FIG. 11C, host vehicle 1105 encounters one or more target vehicles1107 entering main roadway 1112 from merge lane 1111. Host vehicle 1105also detects target vehicles 1109 traveling in a lane adjacent to thelane of the host vehicle. The host vehicle also detects one or moretarget vehicles 1110 traveling in the same lane as host vehicle 1105. Inthis situation, driving policy module 803 may decide to adjust the speedof host vehicle 1105 to give way to target vehicle 1107 and to proceedahead of target vehicle 1115. This can be accomplished, for example, byprogressing to select gap node 919, which, in turn, will select a gapbetween ID0 (vehicle 1107) and ID1 (vehicle 1115) as the appropriatemerging gap. In such a case, the appropriate gap of the mergingsituation defines the objective for a trajectory planner optimizationproblem.

As discussed above, nodes of the options graph may declare themselves as“critical,” which may ensure that the selected option passes through thecritical nodes. Formally, each node may implement a function isCritical.After performing a forward pass on the options graph, from the root to aleaf, and solving the optimization problem of the trajectory planner, abackward pass may be performed from the leaf back to the root. Alongthis backward pass, the IsCritical function of all nodes in the pass maybe called, and a list of all critical nodes may be saved. In the forwardpath corresponding to the next time frame, driving policy module 803 maybe required to choose a path from the root node to a leaf that goesthrough all critical nodes.

FIGS. 11A-11C may be used to show a potential benefit of this approach.For example, in a situation where an overtake action is initiated, anddriving policy module 803 arrives at the leaf corresponding to IDk, itwould be undesirable to choose, for example, the stay node 909 when thehost vehicle is in the middle of the takeover maneuver. To avoid suchjumpiness, the IDj node can designate itself as critical. During themaneuver, the success of the trajectory planner can be monitored, andfunction IsCritical will return a “True” value if the overtake maneuverprogresses as intended. This approach may ensure that in the next timeframe, the takeover maneuver will be continued (rather than jumping toanother, potentially inconsistent maneuver prior to completion of theinitially selected maneuver). If, on the other hand, monitoring of themaneuver indicates that the selected maneuver progressing as intended,or if the maneuver has become unnecessary or impossible, the functionIsCritical can return a “False” value. This can allow the select gapnode to select a different gap in the next time frame, or to abort theovertake maneuver altogether. This approach may allow, on one hand,declaration of the desired path on the options graph at each time step,while on the other hand, may help to promote stability of the policywhile in critical parts of the execution.

Hard constraints, which will be discussed in more detail below, may bedifferentiated from navigational desires. For example, hard constraintsmay ensure safe driving by applying an added layer of filtering of aplanned navigational action. The implicated hard constraints, which maybe programmed and defined manually, rather than through use of a trainedsystem built upon reinforcement learning, can be determined from thesensed state. In some embodiments, however, the trained system may learnthe applicable hard constraints to be applied and followed. Such anapproach may promote driving policy module 803 arriving at a selectedaction that is already in compliance with the applicable hardconstraints, which may reduce or eliminate selected actions that mayrequire later modification to comply with applicable hard constraints.Nevertheless, as a redundant safety measure, hard constraints may beapplied to the output of driving policy module 803 even where drivingpolicy module 803 has been trained to account for predetermined hardconstraints.

There are many examples of potential hard constraints. For example, ahard constraint may be defined in conjunction with a guardrail on anedge of a road. In no situation may the host vehicle be allowed to passthe guardrail. Such a rule induces a hard lateral constraint on thetrajectory of the host vehicle. Another example of a hard constraint mayinclude a road bump (e.g., a speed control bump), which may induce ahard constraint on the speed of driving before the bump and whiletraversing the bump. Hard constraints may be considered safety criticaland, therefore, may be defined manually rather than relying solely on atrained system learning the constraints during training.

In contrast to hard constraints, the goal of desires may be to enable orachieve comfortable driving. As discussed above, an example of a desiremay include a goal of positioning the host vehicle at a lateral positionwithin a lane that corresponds to the center of the host vehicle lane.Another desire may include the ID of a gap to fit into. Note that thereis not a requirement for the host vehicle to be exactly in the center ofthe lane, but instead a desire to be as close as possible to it mayensure that the host vehicle tends to migrate to the center of the laneeven in the event of deviations from the center of the lane. Desires maynot be safety critical. In some embodiments, desires may requirenegotiation with other drivers and pedestrians. One approach forconstructing the desires may rely on the options graph, and the policyimplemented in at least some nodes of the graph may be based onreinforcement learning.

For the nodes of options graph 901 or 1000 implemented as nodes trainedbased on learning, the training process may include decomposing theproblem into a supervised learning phase and a reinforcement learningphase. In the supervised learning phase, a differentiable mapping from(s_(t), a_(t)) to ŝ_(t+1) can be learned such that ŝ_(t+1)≈s_(t+1). Thismay be similar to “model-based” reinforcement learning. However, in theforward loop of the network, ŝ_(t+1) may be replaced by the actual valueof s_(t+1), therefore eliminating problem of error accumulation. Therole of prediction of {umlaut over (s)}_(t+1) is to propagate messagesfrom the future back to past actions. In this sense, the algorithm maybe a combination of “model-based” reinforcement learning with“policy-based learning.”

An important element that may be provided in some scenarios is adifferentiable path from future losses/rewards back to decisions onactions. With the option graph structure, the implementation of optionsthat involve safety constraints are usually not differentiable. Toovercome this issue, the choice of a child in a learned policy node maybe stochastic. That is, a node may output a probability vector, p, thatassigns probabilities used in choosing each of the children of theparticular node. Suppose that a node has k children and let a⁽¹⁾, . . ., a_((k)) be the actions of the path from each child to a leaf. Theresulting predicted action is therefore {dot over (a)}=Σ_(i=1)^(k)p_(i)a^((i)), which may result in a differentiable path from theaction top. In practice, an action a may be chosen to be a_((i)) fori˜p, and the difference between a and a may be referred to as additivenoise.

For the training of ŝ_(t+1) given s_(t), a_(i), supervised learning maybe used together with real data. For training the policy of nodessimulators can be used. Later, fine tuning of a policy can beaccomplished using real data. Two concepts may make the simulation morerealistic. First, using imitation, an initial policy can be constructedusing the “behavior cloning” paradigm, using large real-world data sets.In some cases, the resulting agents may be suitable. In other cases, theresulting agents at least form very good initial policies for the otheragents on the roads. Second, using self-play, our own policy may be usedto augment the training. For example, given an initial implementation ofthe other agents (cars/pedestrians) that may be experienced, a policymay be trained based on a simulator. Some of the other agents may bereplaced with the new policy, and the process may be repeated. As aresult, the policy can continue to improve as it should respond to alarger variety of other agents that have differing levels ofsophistication.

Further, in some embodiments, the system may implement a multi-agentapproach. For example, the system may take into account data fromvarious sources and/or images capturing from multiple angles. Further,some disclosed embodiments may provide economy of energy, asanticipation of an event which does not directly involve the hostvehicle, but which may have an effect on the host vehicle can beconsidered, or even anticipation of an event that may lead tounpredictable circumstances involving other vehicles may be aconsideration (e.g., radar may “see through” the leading vehicle andanticipation of an unavoidable, or even a high likelihood of an eventthat will affect the host vehicle).

Trained System with Imposed Navigational Constraints

In the context of autonomous driving, a significant concern is how toensure that a learned policy of a trained navigational network will besafe. In some embodiments, the driving policy system may be trainedusing constraints, such that the actions selected by the trained systemmay already account for applicable safety constraints. Additionally, insome embodiments, an extra layer of safety may be provided by passingthe selected actions of the trained system through one or more hardconstraints implicated by a particular sensed scene in the environmentof the host vehicle. Such an approach may ensure that that the actionstaken by the host vehicle have been restricted to those confirmed assatisfying applicable safety constraints.

At its core, the navigational system may include a learning algorithmbased on a policy function that maps an observed state to one or moredesired actions. In some implementations, the learning algorithm is adeep learning algorithm. The desired actions may include at least oneaction expected to maximize an anticipated reward for a vehicle. Whilein some cases, the actual action taken by the vehicle may correspond toone of the desired actions, in other cases, the actual action taken maybe determined based on the observed state, one or more desired actions,and non-learned, hard constraints (e.g., safety constraints) imposed onthe learning navigational engine. These constraints may include no-drivezones surrounding various types of detected objects (e.g., targetvehicles, pedestrians, stationary objects on the side of a road or in aroadway, moving objects on the side of a road or in a roadway, guardrails, etc.) In some cases, the size of the zone may vary based on adetected motion (e.g., speed and/or direction) of a detected object.Other constraints may include a maximum speed of travel when passingwithin an influence zone of a pedestrian, a maximum deceleration (toaccount for a target vehicle spacing behind the host vehicle), amandatory stop at a sensed crosswalk or railroad crossing, etc.

Hard constraints used in conjunction with a system trained throughmachine learning may offer a degree of safety in autonomous driving thatmay surpass a degree of safety available based on the output of thetrained system alone. For example, the machine learning system may betrained using a desired set of constraints as training guidelines and,therefore, the trained system may select an action in response to asensed navigational state that accounts for and adheres to thelimitations of applicable navigational constraints. Still, however, thetrained system has some flexibility in selecting navigational actionsand, therefore, there may exist at least some situations in which anaction selected by the trained system may not strictly adhere torelevant navigational constraints. Therefore, in order to require that aselected action strictly adheres to relevant navigational constraints,the output of the trained system may be combined with, compared to,filtered with, adjusted, modified, etc. using a non-machine learningcomponent outside the learning/trained framework that guarantees strictapplication of relevant navigational constraints.

The following discussion provides additional details regarding thetrained system and the potential benefits (especially from a safetyperspective) that may be gleaned from combining a trained system with analgorithmic component outside of the trained/learning framework. Asdiscussed, the reinforcement learning objective by policy may beoptimized through stochastic gradient ascent. The objective (e.g., theexpected reward) may be defined as

_(s˜P) _(o) R(s).

Objectives that involve expectation may be used in machine learningscenarios. Such an objective, without being bound by navigationalconstraints, however, may not return actions strictly bound by thoseconstraints. For example, considering a reward function for whichR(s)=−r for trajectories that represent a rare “corner” event to beavoided (e.g., such as an accident), and R(s)∈|−1, 1| for the rest ofthe trajectories, one goal for the learning system may be to learn toperform an overtake maneuver. Normally, in an accident free trajectory,R(s) would reward successful, smooth, takeovers and penalize staying ina lane without completing the takeover—hence the range [−1, 1]. If asequence, s, represents an accident, the reward, −r, should provide asufficiently high penalty to discourage such an occurrence. The questionis what should be the value of r to ensure accident-free driving.

Observe that the effect of an accident on

[

(s)] is the additive term −pr where p is the probability mass oftrajectories with an accident event. If this term is negligible, i.e.,p<<⊥/τ, then the learning system may prefer a policy that performs anaccident (or adopt in general a reckless driving policy) in order tofulfill the takeover maneuver successfully more often than a policy thatwould be more defensive at the expense of having some takeover maneuversnot complete successfully. In other words, if the probability ofaccidents is to be at most p, then r must be set such that r>>⊥/p. Itmay be desireable to make p extremely small (e.g., on the order ofp=10⁻⁹). Therefore, r should be large. In policy gradient, the gradientof

[

(s)] may be estimated. The following lemma shows that the variance ofthe random variable

(s) grows with pr², which is larger than r for r>>⊥/p. Therefore,estimating the objective may be difficult, and estimating its gradientmay be even more difficult.

Lemma: Let π_(o) be a policy and let p and r be scalars such that withprobability p, R(s)=−r is obtained, and with probability 1−p we haveR(s)∈|−⊥, ⊥] obtained. Then,

Var[

( s )|≥pr ²−(pr+(1−p))²=(p−p ²)r ²−2p(1−p_r−(1−p)² ≈pr ²

where the last approximation holds for the case r≥1/p.

This discussion shows that an objection of the form

[

(s)] may not ensure functional safety without causing a varianceproblem. The baseline subtraction method for variance reduction may notoffer a sufficient remedy to the problem because the problem would shillfrom a high variance of R(s) to an equally high variance of the baselineconstants whose estimation would equally suffer numeric instabilities.Moreover, if the probability of an accident is p, then on average atleast 1/p sequences should be sampled before obtaining an accidentevent. This implies a lower bound of 1/p samples of sequences for alearning algorithm that aims at minimizing

[

(s)]. The solution to this problem may be found in the architecturaldesign described herein, rather than through numerical conditioningtechniques. The approach here is based on the notion that hardconstraints should be injected outside of the learning framework. Inother words, the policy function may be decomposed into a learnable partand a non-learnable part. Formally, the policy function may bestructured as π_(θ)=π^((T))oπ_(θ) ^((D)), where π_(θ) ^((D)) maps the(agnostic) state space into a set of Desires (e.g., desired navigationalgoals, etc.), while π^((ℑ′)) maps the Desires into a trajectory (whichmay determine how the car should move in a short range). The functionπ_(θ) ^((D)) is responsible for the comfort of driving and for makingstrategic decisions such as which other cars should be over-taken orgiven way and what is the desired position of the host vehicle withinits lane, etc. The mapping from sensed navigational state to Desires isa policy π_(θ) ^((D)) that may be learned from experience by maximizingan expected reward. The desires produced by π_(θ) ^((D)) may betranslated into a cost function over driving trajectories. The functionπ^((T)), not a learned function, may be implemented by finding atrajectory that minimizes the cost subject to hard constraints onfunctional safety. This decomposition may ensure functional safety whileat the same time providing for comfortable driving.

A double merge navigational situation, as depicted in FIG. 11D, providesan example further illustrating these concepts. In a double merge,vehicles approach the merge area 1130 from both left and right sides.And, from each side, a vehicle, such as vehicle 1133 or vehicle 1135,can decide whether to merge into lanes on the other side of merge area1130. Successfully executing a double merge in busy traffic may requiresignificant negotiation skills and experience and may be difficult toexecute in a heuristic or brute force approach by enumerating allpossible trajectories that could be taken by all agents in the scene. Inthis double merge example, a set of Desires,

, appropriate for the double merge maneuver may be defined.

may be the Cartesian product of the following sets:

=|0, v_(max)|×L×{g, t₁ o}^(n), where [0, v_(max)] is the desired targetspeed of the host vehicle, L={1, 1.5, 2, 2.5, 3, 3.5, 4} is the desiredlateral position in lane units where whole numbers designate a lanecenter and fractional numbers designate lane boundaries, and {g, t, o}are classification labels assigned to each of the n other vehicles. Theother vehicles may be assigned “g” if the host vehicle is to give way tothe other vehicle, “t” if the host vehicle is to take way relative tothe other vehicle, or “o” if the host vehicle is to maintain an offsetdistance relative to the other vehicle.

Below is a description of how a set of Desires, t{v, l, c₁, . . . ,c_(n)}∈

, may be translated into a cost function over driving trajectories. Adriving trajectory may be represented by (x₁, y₁), . . . ⁻, (x_(k) ⁻,y_(k)) where (x_(i), y_(i)) (lateral, longitudinal) location of the hostvehicle (in ego-centric units) at time τ·i. In some experiments, τ=0.1sec and k=10. Of course, other values may be selected as well. The costassigned to a trajectory may include a weighted sum of individual costsassigned to the desired speed, lateral position, and the label assignedto each of the other n vehicles.

Given a desired speed v∈[0, v_(max)], the cost of a trajectoryassociated with speed is

Σ_(i=2) ^(k)(v−∥(x _(i) y _(i))−(x _(i−1) ,y _(i−1))∥/τ)².

Given desired lateral position, l∈L, the cost associated with desiredlateral position is

Σ_(i=1) ^(k)dist(x _(i) ,y _(i) l)

where dist(x, y, l) is the distance from the point (x, y) to the laneposition l. Regarding the cost due to other vehicles, for any othervehicle (x′₁, y′₁), . . . , (x′_(k), y′_(k)) may represent the othervehicle in egocentric units of the host vehicle, and i may be theearliest point for which there exists j such that the distance between(x_(i), y_(i)) and (x′_(j), y′_(j)) is small. If there is no such point,then i can be set as i=∞. If another car is classified as “give-way”, itmay be desirable that τi>τj+0.5, meaning that the host vehicle willarrive to the trajectory intersection point at least 0.5 seconds afterthe other vehicle will arrive at the same point. A possible formula fortranslating the above constraint into a cost is [τ(j−i)+0.5]₊.

Likewise, if another car is classified as “take-way”, it may bedesirable that τj>τi+0.5, which may be translated to the cost[τ(i−j)+0.5]₊. If another car is classified as “offset”, it may bedesirable that i=∞, meaning that the trajectory of the host vehicle andthe trajectory of the offset car do not intersect. This condition can betranslated to a cost by penalizing with respect to the distance betweentrajectories.

Assigning a weight to each of these costs may provide a single objectivefunction for the trajectory planner; π^((T)). A cost that encouragessmooth driving may be added to the objective.

And, to ensure functional safety of the trajectory, hard constraints canbe added to the objective. For example, (x_(i),y_(i)) may be prohibitedfrom being off the roadway, and (x_(i),y_(i)) may be forbidden frombeing close to (x′_(j), y′_(j)) for any trajectory point (x′_(i),y′_(j)) of any other vehicle if |i−j| is small.

To summarize, the policy, π_(θ), can be decomposed into a mapping fromthe agnostic state to a set of Desires and a mapping from the Desires toan actual trajectory. The latter mapping is not based on learning andmay be implemented by solving an optimization problem whose cost dependson the Desires and whose hard constraints may guarantee functionalsafety of the policy.

The following discussion describes mapping from the agnostic state tothe set of Desires. As described above, to be compliant with functionalsafety, a system reliant upon reinforcement learning alone may suffer ahigh and unwieldy variance on the reward

R(s). This result may be avoided by decomposing the problem into amapping from (agnostic) state space to a set of Desires using policygradient iterations followed by a mapping to an actual trajectory whichdoes not involve a system trained based on machine learning.

For various reasons, the decision making may be further decomposed intosemantically meaningful components. For example, the size of

might be large and even continuous. In the double-merge scenariodescribed above with respect to FIG. 11D,

=[0, v_(max)]×L×{g, t, o}^(n)). Additionally, the gradient estimator mayinvolve the term Σ_(t=1) ^(T) ∇_(θ)π_(θ)(a_(l)|s_(l)). In such anexpression, the variance may grow with the time horizon T. In somecases, the value of T may be roughly 250 which may be high enough tocreate significant variance. Supposing a sampling rate is in the rangeof 10 Hz and the merge area 1130 is 100 meters, preparation for themerge may begin approximately 300 meters before the merge area. IF thehost vehicle travels at 16 meters per second (about 60 km per hour),then the value of T for an episode may be roughly 250.

Returning to the concept of an options graph, an options graph that maybe representative of the double merge scenario depicted in FIG. 11D isshown in FIG. 11E. As previously discussed, an options graph mayrepresent a hierarchical set of decisions organized as a DirectedAcyclic Graph (DAG). There may be a special node in the graph called the“root” node 1140, which may be the only node that has no incoming edges(e.g., decision lines). The decision process may traverse the graph,starting from the root node, until it reaches a “leaf” node, namely, anode that has no outgoing edges. Each internal node may implement apolicy function that chooses a child from among its available children.There may be a predefined mapping from the set of traversals overoptions graph to the set of desires,

. In other words, a traversal on the options graph may be automaticallytranslated into a desire in

. Given a node, v, in the graph, a parameter vector θ_(v) may specifythe policy of choosing a child of v. If Θ is the concatenation of allthe Θ_(v), then π₀ ^((D)) may be defined by traversing from the root ofthe graph to a leaf, while at each node v using the policy defined byΘ_(v), to choose a child node.

In the double merge options graph 1139 of FIG. 11E, root node 1140 mayfirst decide if the host vehicle is within the merging area (e.g., area1130 of FIG. 11D) or if the host vehicle instead is approaching themerging area and needs to prepare for a possible merge. In both cases,the host vehicle may need to decide whether to change lanes (e.g., tothe left or to the right side) or whether to stay in the current lane.If the host vehicle has decided to change lanes, the host vehicle mayneed to decide whether conditions are suitable to go on and perform thelane change maneuver (e.g., at “go” node 1142). If it is not possible tochange lanes, the host vehicle may attempt to “push” toward the desiredlane (e.g., at node 1144 as part of a negotiation with vehicles in thedesired lane) by aiming at being on the lane mark. Alternatively, thehost vehicle may opt to “stay” in the same lane (e.g., at node 1146).Such a process may determine the lateral position for the host vehiclein a natural way. For example,

This may enable determination of the desired lateral position in anatural way. For example, if the host vehicle changes lanes from lane 2to lane 3, the “go” node may set the desired lateral position to 3, the“slay” node may set the desired lateral position to 2, and the “push”node may set the desired lateral position to 2.5. Next, the host vehiclemay decide whether to maintain the “same” speed (node 1148),“accelerate” (node 1150), or “decelerate” (node 1152). Next, the hostvehicle may enter a “chain like” structure 1154 that goes over the othervehicles and sets their semantic meaning to a value in the set {g, t,o}. This process may set the desires relative to the other vehicles. Theparameters of all nodes in this chain may be shared (similar toRecurrent Neural Networks).

A potential benefit of the options is the interpretability of theresults. Another potential benefit is that the decomposable structure ofthe set

can be relied upon and, therefore, the policy at each node may be chosenfrom among a small number of possibilities. Additionally, the structuremay allow for a reduction in the variance of the policy gradientestimator.

As discussed above, the length of an episode in the double mergescenario may be roughly T=250 steps. Such a value (or any other suitablevalue depending on a particular navigational scenario) may provideenough time to see the consequences of the host vehicle actions (e.g.,if the host vehicle decided to change lanes as a preparation for themerge, the host vehicle will see the benefit only after a successfulcompletion of the merge). On the other hand, due to the dynamic ofdriving, the host vehicle must make decisions at a fast enough frequency(e.g., 10 Hz in the case described above).

The options graph may enable a decrease in the effective value of T inat least two ways. First, given higher level decisions, a reward can bedefined for lower level decisions while taking into account shorterepisodes. For example, when the host vehicle has already chosen a “lanechange” and the “go” node, a policy can be learned for assigningsemantic meaning to vehicles by looking at episodes of 2-3 seconds(meaning that T becomes 20-30 instead of 250). Second, for high leveldecisions (such as whether to change lanes or to stay in the same lane),the host vehicle may not need to make decisions every 0.1 seconds.Instead, the host vehicle may be able to either make decisions at alower frequency (e.g., every second), or implement an “optiontermination” function, and then the gradient may be calculated onlyafter every termination of the option. In both cases, the effectivevalue of T may be an order of magnitude smaller than its original value.All in all, the estimator at every node may depend on a value of T whichis an order of magnitude smaller than the original 250 steps, which mayimmediately transfer to a smaller variance.

As discussed above, hard constraints may promote safer driving, andthere may be several different types of constraints. For example, statichard constraints may be defined directly from the sensing state. Thesemay include speed bumps, speed limits, road curvature, junctions, etc.,within the environment of the host vehicle that may implicate one ormore constraints on vehicle speed, heading, acceleration, breaking(deceleration), etc. Static hard constraints may also include semanticfree space where the host vehicle is prohibited from going outside ofthe free space and from navigating too close to physical barriers, forexample. Static hard constraints may also limit (e.g., prohibit)maneuvers that do not comply with various aspects of a kinematic motionof the vehicle, for example, a static hard constraint can be used toprohibit maneuvers that might lead to the host vehicle overturning,sliding, or otherwise losing control.

Hard constraints may also be associated with vehicles. For example, aconstraint may be employed requiring that a vehicle maintain alongitudinal distance to other vehicles of at least one meter and alateral distance from other vehicles of at least 0.5 meters. Constraintsmay also be applied such that the host vehicle will avoid maintaining acollision course with one or more other vehicles. For example, a time τmay be a measure of time based on a particular scene. The predictedtrajectories of the host vehicle and one or more other vehicles may beconsidered from a current time to time τ. Where the two trajectoriesintersect, (t_(i) ^(a), t_(i) ^(l)) may represent the time of arrivaland the leaving time of vehicle i to the intersection point. That is,each car will arrive at point when a first part of the car passes theintersection point, and a certain amount of time will be required beforethe last part of the car passes through the intersection point. Thisamount of time separates the arrival time from the leaving time.Assuming that t₁ ^(a)<t₂ ^(a) (i.e., that the arrival time of vehicle 1is less than the arrival time of vehicle 2), then we will want to ensurethat vehicle 1 has left the intersection point prior to vehicle 2arriving. Otherwise, a collision would result. Thus, a hard constraintmay be implemented such that t₁ ^(t)>t₂ ^(a). Moreover, to ensure thatvehicle 1 and vehicle 2 do not miss one another by a minimal amount, anadded margin of safety may be obtained by including a buffer time intothe constraint (e.g., 0.5 seconds or another suitable value). A hardconstraint relating to predicted intersection trajectories of twovehicles may be expressed as t₁ ^(l)>t₂ ^(a)+0.5.

The amount of time τ over which the trajectories of the host vehicle andone or more other vehicles are tracked may vary. In junction scenarios,however, where speeds may be lower, τ may be longer, and τ may bedefined such that a host vehicle will enter and leave the junction inless than seconds.

Applying hard constraints to vehicle trajectories, of course, requiresthat the trajectories of those vehicles be predicted. For the hostvehicle, trajectory prediction may be relatively straightforward, as thehost vehicle generally already understands and, indeed, is planning anintended trajectory at any given time. Relative to other vehicles,predicting their trajectories can be less straightforward. For othervehicles, the baseline calculation for determining predictedtrajectories may rely on the current speed and heading of the othervehicles, as determined, for example, based on analysis of an imagestream captured by one or more cameras and/or other sensors (radar,lidar, acoustic, etc.) aboard the host vehicle.

There can be some exceptions, however, that can simplify the problem orat least provide added confidence in a trajectory predicted for anothervehicle. For example, with respect to structured roads in which there isan indication of lanes and where give-way rules may exist, thetrajectories of other vehicles can be based, at least in part, upon theposition of the other vehicles relative to the lanes and based uponapplicable give-way rules. Thus, in some situations, when there areobserved lane structures, it may be assumed that next-lane vehicles willrespect lane boundaries. That is, the host vehicle may assume that anext-lane vehicle will stay in its lane unless there is observedevidence (e.g., a signal light, strong lateral movement, movement acrossa lane boundary) indicating that the next-lane vehicle will cut into thelane of the host vehicle.

Other situations may also provide clues regarding the expectedtrajectories of other vehicles. For example, at stop signs, trafficlights, roundabouts, etc., where the host vehicle may have the right ofway, it may be assumed that other vehicles will respect that right ofway. Thus, unless there is observed evidence of a rule break, othervehicles may be assumed to proceed along a trajectory that respects therights of way possessed by the host vehicle.

Hard constraints may also be applied with respect to pedestrians in anenvironment of the host vehicle. For example, a buffer distance may beestablished with respect to pedestrians such that the host vehicle isprohibited from navigating any closer than the prescribed bufferdistance relative to any observed pedestrian. The pedestrian bufferdistance may be any suitable distance. In some embodiments, the bufferdistance may be at least one meter relative to an observed pedestrian.

Similar to the situation with vehicles, hard constraints may also beapplied with respect to relative motion between pedestrians and the hostvehicle. For example, the trajectory of a pedestrian (based on a headingdirection and speed) may be monitored relative to the projectedtrajectory of the host vehicle. Given a particular pedestriantrajectory, with every point p on the trajectory, t(p) may represent thetime required for the pedestrian to reach point p. To maintain therequired buffer distance of at least J meter from the pedestrian, eithert(p) must be larger than the time the host vehicle will reach point p(with sufficient difference in time such that the host vehicle passes infront of the pedestrian by a distance of at least one meter) or thatt(p) must be less than the time the host vehicle will reach point p(e.g., if the host vehicle brakes to give way to the pedestrian). Still,in the latter example, the hard constraint may require that the hostvehicle arrive at point p at a sufficient time later than the pedestriansuch that the host vehicle can pass behind the pedestrian and maintainthe required buffer distance of at least one meter. Of course, there maybe exceptions to the pedestrian hard constraint. For example, where thehost vehicle has the right of way or where speeds are very slow, andthere is no observed evidence that the pedestrian will decline to giveway to the host vehicle or will otherwise navigate toward the hostvehicle, the pedestrian hard constraint may be relaxed (e.g., to asmaller buffer of at least 0.75 meters or 0.50 meters).

In some examples, constraints may be relaxed where it is determined thatnot all can be met. For example, in situations where a road is toonarrow to leave desired spacing (e.g., 0.5 meters) from both curbs orfrom a curb and a parked vehicle, one or more the constraints may berelaxed if there are mitigating circumstances. For example, if there areno pedestrians (or other objects) on the sidewalk one can proceed slowlyat 0.1 meters from a curb. In some embodiments, constraints may berelaxed if doing so will improve the user experience. For example, inorder to avoid a pothole, constraints may be relaxed to allow a vehicleto navigate closers to the edges of the lane, a curb, or a pedestrianmore than might ordinarily be permitted. Furthermore, when determiningwhich constrains to relax, in some embodiments, the one or moreconstraints chosen to relax are those deemed to have the least availablenegative impact to safety. For example, a constraint relating to howclose the vehicle may travel to the curb or to a concrete barrier may berelaxed before relaxing one dealing with proximity to other vehicles. Insome embodiments, pedestrian constraints may be the last to be relaxed,or may never be relaxed in some situations.

FIG. 12 shows an example of a scene that may be captured and analyzedduring navigation of a host vehicle. For example, a host vehicle mayinclude a navigation system (e.g., system 100), as described above, thatmay receive from a camera (e.g., at least one of image capture device122, image capture device 124, and image capture device 126) associatedwith the host vehicle a plurality of images representative of anenvironment of the host vehicle. The scene shown in FIG. 12 is anexample of one of the images that may be captured at time z from anenvironment of a host vehicle traveling in lane 1210 along a predictedtrajectory 1212. The navigation system may include at least oneprocessing device (e.g., including any of the EyeQ processors or otherdevices described above) that are specifically programmed to receive theplurality of images and analyze the images to determine an action inresponse to the scene. Specifically, the at least one processing devicemay implement sensing module 801, driving policy module 803, and controlmodule 805, as shown in FIG. 8. Sensing module 801 may be responsiblefor collecting and outputting the image information collected from thecameras and providing that information, in the form of an identifiednavigational stale, to driving policy module 803, which may constitute atrained navigational system that has been trained through machinelearning techniques, such as supervised learning, reinforcementlearning, etc. Based on the navigational state information provided todriving policy module 803 by sensing module 801, driving policy module803 (e.g., by implementing the options graph approach described above)may generate a desired navigational action for execution by the hostvehicle in response to the identified navigational state.

In some embodiments, the at least one processing device may translatethe desired navigation action directly into navigational commands using,for example, control module 805. In other embodiments, however, hardconstraints may be applied such that the desired navigational actionprovided by the driving policy module 803 is tested against variouspredetermined navigational constraints that may be implicated by thescene and the desired navigational action. For example, where drivingpolicy module 803 outputs a desired navigational action that would causethe host vehicle to follow trajectory 1212, this navigational action maybe tested relative to one or more hard constraints associated withvarious aspects of the environment of the host vehicle. For example, acaptured image 1201 may reveal a curb 1213, a pedestrian 1215, a targetvehicle 1217, and a stationary object (e.g., an overturned box) presentin the scene. Each of these may be associated with one or more hardconstraints. For example, curb 1213 may be associated with a staticconstraint that prohibits the host vehicle from navigating into the curbor past the curb and onto a sidewalk 1214. Curb 1213 may also beassociated with a road barrier envelope that defines a distance (e.g., abuffer zone) extending away from (e.g., by 0.1 meters, 0.25 meters, 0.5meters, 1 meter, etc.) and along the curb, which defines a no-navigatezone for the host vehicle. Of course, static constraints may beassociated with other types of roadside boundaries as well (e.g., guardrails, concrete pillars, traffic cones, pylons, or any other type ofroadside barrier).

It should be noted that distances and ranging may be determined by anysuitable method. For example, in some embodiments, distance informationmay be provided by onboard radar and/or lidar systems. Alternatively oradditionally, distance information may be derived from analysis of oneor more images captured from the environment of the host vehicle. Forexample, numbers of pixels of a recognized object represented in animage may be determined and compared to known field of view and focallength geometries of the image capture devices to determine scale anddistances. Velocities and accelerations may be determined, for example,by observing changes in scale between objects from image to image overknown time intervals. This analysis may indicate the direction ofmovement toward or away from the host vehicle along with how fast theobject is pulling away from or corning toward the host vehicle. Crossingvelocity may be determined through analysis of the change in an object'sX coordinate position from one image to another over known time periods.

Pedestrian 1215 may be associated with a pedestrian envelope thatdefines a buffer zone 1216. In some cases, an imposed hard constraintmay prohibit the host vehicle from navigating within a distance of 1meter from pedestrian 1215 (in any direction relative to thepedestrian). Pedestrian 1215 may also define the location of apedestrian influence zone 1220. Such an influence zone may be associatedwith a constraint that limits the speed of the host vehicle within theinfluence zone. The influence zone may extend 5 meters, 10 meters, 20meters, etc., from pedestrian 1215. Each graduation of the influencezone may be associated with a different speed limit. For example, withina zone of 1 meter to five meters from pedestrian 1215, host vehicle maybe limited to a first speed (e.g., 10 mph, 20 mph, etc.) that may beless than a speed limit in a pedestrian influence zone extending from 5meters to 10 meters. Any graduation for the various stages of theinfluence zone may be used. In some embodiments, the first stage may benarrower than from 1 meter to five meters and may extend only from onemeter to two meters. In other embodiments, the first stage of theinfluence zone may extend from 1 meter (the boundary of the no-navigatezone around a pedestrian) to a distance of at least 10 meters. A secondstage, in turn, may extend from 10 meters to at least about 20 meters.The second stage may be associated with a maximum rate of travel for thehost vehicle that is greater than the maximum rate of travel associatedwith the first stage of the pedestrian influence zone.

One or more stationary object constraints may also be implicated by thedetected scene in the environment of the host vehicle. For example, inimage 1201, the at least one processing device may detect a stationaryobject, such as box 1219 present in the roadway. Detected stationaryobjects may include various objects, such as at least one of a tree, apole, a road sign, or an object in a roadway. One or more predefinednavigational constraints may be associated with the detected stationaryobject. For example, such constraints may include a stationary objectenvelope, wherein the stationary object envelope defines a buffer zoneabout the object within which navigation of the host vehicle may beprohibited. At least a portion of the buffer zone may extend apredetermined distance from an edge of the detected stationary object.For example, in the scene represented by image 1201, a buffer zone of atleast 0.1 meters, 0.25 meters, 0.5 meters or more may be associated withbox 1219 such that the host vehicle will pass to the right or to theleft of the box by at least some distance (e.g., the buffer zonedistance) in order to avoid a collision with the detected stationaryobject.

The predefined hard constraints may also include one or more targetvehicle constraints. For example, a target vehicle 1217 may be detectedin image 1201. To ensure that the host vehicle does not collide withtarget vehicle 1217, one or more hard constraints may be employed. Insome eases, a target vehicle envelope may be associated with a singlebuffer zone distance. For example, the buffer zone may be defined by a 1meter distance surrounding the target vehicle in all directions. Thebuffer zone may define a region extending from the target vehicle by atleast one meter into which the host vehicle is prohibited fromnavigating.

The envelope surrounding target vehicle 1217 need not be defined by afixed buffer distance, however. In some cases the predefined hardconstraints associate with target vehicles (or any other movable objectsdetected in the environment of the host vehicle) may depend on theorientation of the host vehicle relative to the detected target vehicle.For example, in some cases, a longitudinal buffer zone distance (e.g.,one extending from the target vehicle toward the front or rear of thehost vehicle—such as in the case that the host vehicle is driving towardthe target vehicle) may be at least one meter. A lateral buffer zonedistance (e.g., one extending from the target vehicle toward either sideof the host vehicle—such as when the host vehicle Ls traveling in a sameor opposite direction as the target vehicle such that a side of the hostvehicle will pass adjacent to a side of the target vehicle) may be atleast 0.5 meters.

As described above, other constraints may also be implicated bydetection of a target vehicle or a pedestrian in the environment of thehost vehicle. For example, the predicted trajectories of the hostvehicle and target vehicle 1217 may be considered and where the twotrajectories intersect (e.g., at intersection point 1230), a hardconstraint may require t₁ ^(t)>t₂ ^(a) or t₁ ^(l)>t₂ ^(a)+0.5 where thehost vehicle is vehicle 1, and target vehicle 1217 is vehicle 2.Similarly, the trajectory of pedestrian 1215 (based on a headingdirection and speed) may be monitored relative to the projectedtrajectory of the host vehicle. Given a particular pedestriantrajectory, with every point p on the trajectory, t(p) will representthe time required for the pedestrian to reach point p (i.e., point 1231in FIG. 12). To maintain the required buffer distance of at least 1meter from the pedestrian, either t(p) must be larger than the time thehost vehicle will reach point p (with sufficient difference in time suchthat the host vehicle passes in front of the pedestrian by a distance ofat least one meter) or that t(p) must be less than the time the hostvehicle will reach point p (e.g., if the host vehicle brakes to give wayto the pedestrian). Still, in the latter example, the hard constraintwill require that the host vehicle arrive at point p at a sufficienttime later than the pedestrian such that the host vehicle can passbehind the pedestrian and maintain the required buffer distance of atleast one meter.

Other hard constraints may also be employed. For example, a maximumdeceleration rate of the host vehicle may be employed in at least somecases. Such a maximum deceleration rate may be determined based on adetected distance to a target vehicle following the host vehicle (e.g.,using images collected from a rearward facing camera). The hardconstraints may include a mandatory stop at a sensed crosswalk or arailroad crossing or other applicable constraints.

Where analysis of a scene in an environment of the host vehicleindicates that one or more predefined navigational constraints may beimplicated, those constraints may be imposed relative to one or moreplanned navigational actions for the host vehicle. For example, whereanalysis of a scene results in driving policy module 803 returning adesired navigational action, that desired navigational action may betested against one or more implicated constraints. If the desirednavigational action is determined to violate any aspect of theimplicated constraints (e.g., if the desired navigational action wouldcarry the host vehicle within a distance of 0.7 meters of pedestrian1215 where a predefined hard constraint requires that the host vehicleremain at least 1.0 meters from pedestrian 1215), then at least onemodification to the desired navigational action may be made based on theone or more predefined navigational constraints. Adjusting the desirednavigational action in this way may provide an actual navigationalaction for the host vehicle in compliance with the constraintsimplicated by a particular scene detected in the environment of the hostvehicle.

After determination of the actual navigational action for the hostvehicle, that navigational action may be implemented by causing at leastone adjustment of a navigational actuator of the host vehicle inresponse to the determined actual navigational action for the hostvehicle. Such navigational actuator may include at least one of asteering mechanism, a brake, or an accelerator of the host vehicle.

Prioritized Constraints

As described above, various hard constraints may be employed with anavigational system to ensure safe operation of a host vehicle. Theconstraints may include a minimum safe driving distance with respect toa pedestrian, a target vehicle, a road harrier, or a detected object, amaximum speed of travel when passing within an influence zone of adetected pedestrian, or a maximum deceleration rate for the hostvehicle, among others. These constraints may be imposed with a trainedsystem trained based on machine learning (supervised, reinforcement, ora combination), but they also may be useful with non-trained systems(e.g., those employing algorithms to directly address anticipatedsituations arising in scenes from a host vehicle environment).

In either case, there may be a hierarchy of constraints. In other words,some navigational constraints may have priority over other constraints.Thus, if a situation arose in which a navigational action was notavailable that would result in ail implicated constraints beingsatisfied, the navigation system may determine the availablenavigational action that achieves the highest priority constraintsfirst. For example, the system may cause the vehicle to avoid apedestrian first even if navigation to avoid the pedestrian would resultin a collision with another vehicle or an object detected in a road. Inanother example, the system may cause the vehicle to ride up on a curbto avoid a pedestrian.

FIG. 13 provides a flowchart illustrating an algorithm for implementinga hierarchy of implicated constraints determined based on analysis of ascene in an environment of a host vehicle. For example, at step 1301, atleast one processing device associated with the navigational system(e.g., an EyeQ processor, etc.) may receive, from a camera mounted onthe host vehicle, a plurality of images representative of an environmentof the host vehicle. Through analysis of an image or imagesrepresentative of the scene of the host vehicle environment at step1303, a navigational state associated with the host vehicle may beidentified. For example, a navigational state may indicate that the hostvehicle is traveling along a two-lane road 1210, as in FIG. 12, that atarget vehicle 1217 is moving through an intersection ahead of the hostvehicle, that a pedestrian 1215 is waiting to cross the road on whichthe host vehicle travels, that an object 1219 is present ahead in thehost vehicle lane, among various other attributes of the scene.

At step 1305, one or more navigational constraints implicated by thenavigational state of the host vehicle may be determined. For example,the at least one processing device, after analyzing a scene in theenvironment of the host vehicle represented by one or more capturedimages may determine one or more navigational constraints implicated byobjects, vehicles, pedestrians, etc., recognized through image analysisof the captured images. In some embodiments, the at least one processingdevice may determine at least a first predefined navigational constraintand a second predefined navigational constraint implicated by thenavigational state, and the first predefined navigational constraint maydiffer from the second predefined navigational constraint. For example,the first navigational constraint may relate to one or more targetvehicles detected in the environment of the host vehicle, and the secondnavigational constraint may relate to a pedestrian detected in theenvironment of the host vehicle.

At step 1307, the at least one processing device nay determine apriority associated with constraints identified in step 1305. In theexample described, the second predefined navigational constraint,relating to pedestrians, may have a priority higher than the firstpredefined navigational constraint, which relates to target vehicles.While priorities associated with navigational constraints may bedetermined or assigned based on various factors, in some embodiments,the priority of a navigational constraint may be related to its relativeimportance from a safety perspective. For example, while it may beimportant that all implemented navigational constraints be followed orsatisfied in as many situations as possible, some constraints may beassociated with greater safety risks than others and, therefore, may beassigned higher priorities. For example, a navigational constraintrequiring that the host vehicle maintain at least a 1 meter spacing froma pedestrian may have a higher priority than a constraint requiring thatthe host vehicle maintain at least a 1 meter spacing from a targetvehicle. This may be because a collision with a pedestrian may have moresevere consequences than a collision with another vehicle. Similarly,maintaining a space between the host vehicle and a target vehicle mayhave a higher priority than a constraint requiring the host vehicle toavoid a box in the road, to drive less than a certain speed over a speedbump, or to expose the host vehicle occupants to no more than a maximumacceleration level.

While driving policy module 803 is designed to maximize safety bysatisfying navigational constraints implicated by a particular scene ornavigational state, in some situations it may be physically impossibleto satisfy every implicated constraint. In such situations, the priorityof each implicated constraint may be used to determine which of theimplicated constraints should be satisfied first, as shown at step 1309.Continuing with the example above, in a situation where it is notpossible satisfy both the pedestrian gap constraint and the targetvehicle gap constraint, but rather only one of the constraints can besatisfied, then the higher priority of the pedestrian gap constraint mayresult in that constraint being satisfied before attempting to maintaina gap to the target vehicle. Thus, in normal situations, the at leastone processing device may determine, based on the identifiednavigational state of the host vehicle, a first navigational action forthe host vehicle satisfying both the first predefined navigationalconstraint and the second predefined navigational constraint where boththe first predefined navigational constraint and the second predefinednavigational constraint can be satisfied, as shown at step 1311. Inother situations, however, where not all the implicated constraints canbe satisfied, the at least one processing device may determine, based onthe identified navigational state, a second navigational action for thehost vehicle satisfying the second predefined navigational constraint(i.e., the higher priority constraint), but not satisfying the firstpredefined navigational constraint (having a priority lower than thesecond navigational constraint), where the first predefined navigationalconstraint and the second predefined navigational constraint cannot bothbe satisfied, as shown at step 1313.

Next, at step 1315, to implement the determined navigational actions forthe host vehicle the at least one processing device can cause at leastone adjustment of a navigational actuator of the host vehicle inresponse to the determined first navigational action or the determinedsecond navigational action for the host vehicle. As in previous example,the navigational actuator may include at least one of a steeringmechanism, a brake, or an accelerator.

Constraint Relaxation

As discussed above, navigational constraints may be imposed for safetypurposes. The constraints may include a minimum safe driving distancewith respect to a pedestrian, a target vehicle, a road harrier, or adetected object, a maximum speed of travel when passing within aninfluence zone of a detected pedestrian, or a maximum deceleration ratefor the host vehicle, among others. These constraints may be imposed ina learning or non-learning navigational system. In certain situations,these constraints may be relaxed. For example, where the host vehicleslows or stops near a pedestrian, then progresses slowly to convey anintention to pass by the pedestrian, a response of the pedestrian can bedetected from acquired images. If the response of the pedestrian is tostay still or to stop moving (and/or if eye contact with the pedestrianis sensed), it may be understood that the pedestrian recognizes anintent of the navigational system to pass by the pedestrian. In suchsituations, the system may relax one or more predefined constraints andimplement a less stringent constraint (e.g., allow the vehicle tonavigate in 0.5 meters of a pedestrian rather than within a morestringent 1 meter boundary).

FIG. 14 provides a flowchart for implementing control of the hostvehicle based on relaxation of one or more navigational constraints. Atstep 1401, the at least one processing device may receive, from a cameraassociated with the host vehicle, a plurality of images representativeof an environment of the host vehicle. Analysis of the images at step1403 may enable identification of a navigational state associated withthe host vehicle. At step 1405, the at least one processor may determinenavigational constraints associated with the navigational state of thehost vehicle. The navigational constraints may include a firstpredefined navigational constraint implicated by at least one aspect ofnavigational state. At step 1407, analysis of the plurality of imagesmay reveal the presence of at least one navigational constraintrelaxation factor.

A navigational constraint relaxation factor may include any suitableindicator that one or more navigational constraints may be suspended,altered, or otherwise relaxed in at least one aspect. In someembodiments, the at least one navigational constraint relaxation factormay include a determination (based on image analysis) that the eyes of apedestrian are looking in a direction of the host vehicle. In suchcases, it may more safely be assumed that the pedestrian is aware of thehost vehicle. As a result, a confidence level may be higher that thepedestrian will not engage in unexpected actions that cause thepedestrian to move into a path of the host vehicle. Other constraintrelaxation factors may also be used. For example, the at least onenavigational constraint relaxation factor may include: a pedestriandetermined to be not moving (e.g., one presumed to be less likely ofentering a path of the host vehicle); or a pedestrian whose motion isdetermined to be slowing. The navigational constraint relaxation factormay also include more complicated actions, such as a pedestriandetermined to be not moving after the host vehicle has come to a stopand then resumed movement. In such a situation, the pedestrian may beassumed to understand that the host vehicle has a right of way, and thepedestrian coming to a stop may suggest an intent of the pedestrian togive way to the host vehicle. Other situations that may cause one ormore constraints to be relaxed include the type of curb stone (e.g., alow curb stone or one with a gradual slope might allow a relaxeddistance constraint), lack of pedestrians or other objects on sidewalk,a vehicle with its engine not running may have a relaxed distance, or asituation in which a pedestrian is facing away and/or is moving awayfrom the area towards which the host vehicle is heading.

Where the presence of a navigational constraint relaxation factor isidentified (e.g., at step 1407), a second navigational constraint may bedetermined or developed in response to detection of the constraintrelaxation factor. This second navigational constraint may be differentfrom the first navigational constraint and may include at least onecharacteristic relaxed with respect to the first navigationalconstraint. The second navigational constraint may include a newlygenerated constraint based on the first constraint, where the newlygenerated constraint includes at least one modification that relaxes thefirst constraint in at least one respect. Alternatively, the secondconstraint may constitute a predetermined constraint that is lessstringent than the first navigational constraint in at least onerespect. In some embodiments, such second constraints may be reservedfor usage only for situations where a constraint relaxation factor isidentified in an environment of the host vehicle. Whether the secondconstraint is newly generated or selected from a set of fully orpartially available predetermined constraints, application of a secondnavigational constraint in place of a more stringent first navigationalconstraint (that may be applied in the absence of detection of relevantnavigational constraint relaxation factors) may be referred to asconstraint relaxation and may be accomplished in step 1409.

Where at least one constraint relaxation factor is detected at step1407, and at least one constraint has been relaxed in step 1409, anavigational action for the host vehicle may be determined at step 1411.The navigational action for the host vehicle may be based on theidentified navigational state and may satisfy the second navigationalconstraint. The navigational action may be implemented at step 1413 bycausing at least one adjustment of a navigational actuator of the hostvehicle in response to the determined navigational action.

As discussed above, the usage of navigational constraints and relaxednavigational constraints may be employed with navigational systems thatare trained (e.g., through machine learning) or untrained (e.g., systemsprogrammed to respond with predetermined actions in response to specificnavigational states). Where trained navigational systems are used, theavailability of relaxed navigational constraints for certainnavigational situations may represent a mode switching from a trainedsystem response to an untrained system response. For example, a trainednavigational network may determine an original navigational action forthe host vehicle, based on the first navigational constraint. The actiontaken by the vehicle, however, may be one that is different from thenavigational action satisfying the first navigational constraint.Rather, the action taken may satisfy the more relaxed secondnavigational constraint and may be an action developed by a non-trainedsystem (e.g., as a response to detection of a particular condition inthe environment of the host vehicle, such as the presence of anavigational constraint relaxation factor).

There are many examples of navigational constraints that may be relaxedin response to detection in the environment of the host vehicle of aconstraint relaxation factor. For example, where a predefinednavigational constraint includes a buffer zone associated with adetected pedestrian, and at least a portion of the buffer zone extends adistance from the detected pedestrian, a relaxed navigational constraint(either newly developed, called up from memory from a predetermined set,or generated as a relaxed version of a preexisting constraint) mayinclude a different or modified buffer zone. For example, the differentor modified buffer zone may have a distance relative to the pedestrianthat is less than the original or unmodified buffer zone relative to thedetected pedestrian. As a result, in view of the relaxed constraint, thehost vehicle may be permitted to navigate closer to a detectedpedestrian, where an appropriate constraint relaxation factor isdetected in the environment of the host vehicle.

A relaxed characteristic of a navigational constraint may include areduced width in a buffer zone associated with at least one pedestrian,as noted above. The relaxed characteristic, however, may also include areduced width in a buffer zone associated with a target vehicle, adetected object, a roadside harrier, or any other object detected in theenvironment of the host vehicle.

The at least one relaxed characteristic may also include other types ofmodifications in navigational constraint characteristics. For example,the relaxed characteristic may include an increase in speed associatedwith at least one predefined navigational constraint. The relaxedcharacteristic may also include an increase in a maximum allowabledeceleration/acceleration associated with at least one predefinednavigational constraint.

While constraints may be relaxed in certain situations, as describedabove, in other situations, navigational constraints may be augmented.For example, in some situations, a navigational system may determinethat conditions warrant augmentation of a normal set of navigationalconstraints. Such augmentation may include adding new constraints to apredefined set of constraints or adjusting one or more aspects of apredefined constraint. The addition or adjustment may result in moreconservative navigation relative the predefined set of constraintsapplicable under normal driving conditions. Conditions that may warrantconstraint augmentation may include sensor failure, adverseenvironmental conditions (rain, snow, fog, or other conditionsassociated with reduced visibility or reduced vehicle traction), etc.

FIG. 15 provides a flowchart for implementing control of the hostvehicle based on augmentation of one or more navigational constraints.At step 1501, the at least one processing device may receive, from acamera associated with the host vehicle, a plurality of imagesrepresentative of an environment of the host vehicle. Analysis of theimages at step 1503 may enable identification of a navigational stateassociated with the host vehicle. At step 1505, the at least oneprocessor may determine navigational constraints associated with thenavigational state of the host vehicle. The navigational constraints mayinclude a first predefined navigational constraint implicated by atleast one aspect of the navigational state. At step 1507, analysis ofthe plurality of images may reveal the presence of at least onenavigational constraint augmentation factor.

An implicated navigational constraint may include any of thenavigational constraints discussed above (e.g., with respect to FIG. 12)or any other suitable navigational constraints. A navigationalconstraint augmentation factor may include any indicator that one ormore navigational constraints may be supplemented/augmented in at leastone aspect. Supplementation or augmentation of navigational constraintsmay be performed on a per set basis (e.g., by adding new navigationalconstraints to a predetermined set of constraints) or may be performedon a per constraint basis (e.g., modifying a particular constraint suchthat the modified constraint is more restrictive than the original, oradding a new constraint that corresponds to a predetermined constraint,wherein the new constraint is more restrictive than the correspondingconstraint in at least one aspect). Additionally, or alternatively,supplementation or augmentation of navigational constraints may referselection from among a set of predetermined constraints based on ahierarchy. For example, a set of augmented constraints may be availablefor selection based on whether a navigational augmentation factor isdetected in the environment of or relative to the host vehicle. Undernormal conditions where no augmentation factor is detected, then theimplicated navigational constraints may be drawn from constraintsapplicable to normal conditions. On the other hand, where one or moreconstraint augmentation factors are detected, the implicated constraintsmay be drawn from augmented constraints either generated or predefinedrelative to the one or more augmentation factors. The augmentedconstraints may be more restrictive in at least one aspect thancorresponding constraints applicable under normal conditions.

In some embodiments, the at least one navigational constraintaugmentation factor may include a detection (e.g., based on imageanalysis) of the presence of ice, snow, or water on a surface of a roadin the environment of the host vehicle. Such a determination may bebased, for example, upon detection of: areas of reflectance higher thanexpected for dry roadways (e.g., indicative of ice or water on theroadway); white regions on the road indicating the presence of snow;shadows on the roadway consistent with the presence of longitudinaltrenches (e.g., tire tracks in snow) on the roadway; water droplets orice/snow particles on a windshield of the host vehicle; or any othersuitable indicator of the presence of water or ice/snow on a surface ofa road.

The at least one navigational constraint augmentation factor may alsoinclude detection of particulates on an outer surface of a windshield ofthe host vehicle. Such particulates may impair image quality of one ormore image capture devices associated with the host vehicle. Whiledescribed with respect to a windshield of the host vehicle, which isrelevant for cameras mounted behind the windshield of the host vehicle,detection of particulates on other surfaces (e.g., a lens or lens coverof a camera, headlight lens, rear windshield, a tail light lens, or anyother surface of the host vehicle visible to an image capture device (ordetected by a sensor) associated with the host vehicle may also indicatethe presence of a navigational constraint augmentation factor.

The navigational constraint augmentation factor may also be detected asan attribute of one or more image acquisition devices. For example, adetected decrease in image quality of one or more images captured by animage capture device (e.g., a camera) associated with the host vehiclemay also constitute a navigational constraint augmentation factor. Adecline in image quality may be associated with a hardware failure orpartial hardware failure associated with the image capture device or anassembly associated with the image capture device. Such a decline inimage quality may also be caused by environmental conditions. Forexample, the presence of smoke, fog, rain, snow, etc., in the airsurrounding the host vehicle may also contribute to reduced imagequality relative to the road, pedestrians, target vehicles, etc., thatmay be present in an environment of the host vehicle.

The navigational constraint augmentation factor may also relate to otheraspects of the host vehicle. For example, in some situations, thenavigational constraint augmentation factor may include a detectedfailure or partial failure of a system or sensor associate with the hostvehicle. Such an augmentation factor may include, for example, detectionof failure or partial failure of a speed sensor, GPS receiver,accelerometer, camera, radar, lidar, brakes, tires, or any other systemassociated with the host vehicle that may impact the ability of the hostvehicle to navigate relative to navigational constraints associated witha navigational state of the host vehicle.

Where the presence of a navigational constraint augmentation factor isidentified (e.g., at step 1507), a second navigational constraint may bedetermined or developed in response to detection of the constraintaugmentation factor. This second navigational constraint may bedifferent from the first navigational constraint and may include atleast one characteristic augmented with respect to the firstnavigational constraint. The second navigational constraint may be morerestrictive than the first navigational constraint, because detection ofa constraint augmentation factor in the environment of the host vehicleor associated with the host vehicle may suggest that the host vehiclemay have at least one navigational capability reduced with respect tonormal operating conditions. Such reduced capabilities may includelowered road traction (e.g., ice, snow, or water on a roadway; reducedtire pressure; etc.); impaired vision (e.g., rain, snow, dust, smoke,fog etc. that reduces captured image quality); impaired detectioncapability (e.g., sensor failure or partial failure, reduced sensorperformance, etc.), or any other reduction in capability of the hostvehicle to navigate in response to a detected navigational state.

Where at least one constraint augmentation factor is detected at step1507, and at least one constraint has been augmented in step 1509, anavigational action for the host vehicle may be determined at step 1511.The navigational action for the host vehicle may be based on theidentified navigational state and may satisfy the second navigational(i.e., augmented) constraint. The navigational action may be implementedat step 1513 by causing at least one adjustment of a navigationalactuator of the host vehicle in response to the determined navigationalaction.

As discussed, the usage of navigational constraints and augmentednavigational constraints may be employed with navigational systems thatare trained (e.g., through machine learning) or untrained (e.g., systemsprogrammed to respond with predetermined actions in response to specificnavigational states). Where trained navigational systems are used, theavailability of augmented navigational constraints for certainnavigational situations may represent a mode switching from a trainedsystem response to an untrained system response. For example, a trainednavigational network may determine an original navigational action forthe host vehicle, based on the first navigational constraint. The actiontaken by the vehicle, however, may be one that is different from thenavigational action satisfying the first navigational constraint.Rather, the action taken may satisfy the augmented second navigationalconstraint and may be an action developed by a non-trained system (e.g.,as a response to detection of a particular condition in the environmentof the host vehicle, such as the presence of a navigational constraintaugmented factor).

There are many examples of navigational constraints that may begenerated, supplemented, or augmented in response to detection in theenvironment of the host vehicle of a constraint augmentation factor. Forexample, where a predefined navigational constraint includes a bufferzone associated with a detected pedestrian, object, vehicle, etc., andat least a portion of the buffer zone extends a distance from thedetected pedestrian/object/vehicle, an augmented navigational constraint(either newly developed, called up from memory from a predetermined set,or generated as an augmented version of a preexisting constraint) mayinclude a different or modified buffer zone. For example, the differentor modified buffer zone may have a distance relative to thepedestrian/object/vehicle that is greater than the original orunmodified buffer zone relative to the detectedpedestrian/object/vehicle. As a result, in view of the augmentedconstraint, the host vehicle may be forced to navigate further from thedetected pedestrian/object/vehicle, where an appropriate constraintaugmentation factor is detected in the environment of the host vehicleor relative to the host vehicle.

The at least one augmented characteristic may also include other typesof modifications in navigational constraint characteristics. Forexample, the augmented characteristic may include a decrease in speedassociated with at least one predefined navigational constraint. Theaugmented characteristic may also include a decrease in a maximumallowable deceleration/acceleration associated with at least onepredefined navigational constraint.

Navigation Based on Long Range Planning

In some embodiments, the disclosed navigational system can respond notonly to a detected navigational state in an environment of the hostvehicle, but may also determine one or more navigational actions basedon long range planning. For example, the system may consider thepotential impact on future navigational states of one or morenavigational actions available as options for navigating with respect toa detected navigational state. Considering the effects of availableactions on future states may enable the navigational system to determinenavigational actions based not just upon a currently detectednavigational state, but also based upon long range planning. Navigationusing long range planning techniques may be especially applicable whereone or more reward functions are employed by the navigation system as atechnique for selecting navigational actions from among availableoptions. Potential rewards may be analyzed with respect to the availablenavigational actions that may be taken in response to a detected,current navigational state of the host vehicle. Further, however, thepotential rewards may also be analyzed relative to actions that may betaken in response to future navigational states projected to result fromthe available actions to a current navigational state. As a result, thedisclosed navigational system may, in some cases, select a navigationalaction in response to a detected navigational state even where theselected navigational action may not yield the highest reward from amongthe available actions that may be taken in response to the currentnavigational state. This may be especially true where the systemdetermines that the selected action may result in a future navigationalstate giving rise to one or more potential navigational actions offeringhigher rewards than the selected action or, in some cases, any of theactions available relative to a current navigational state. Theprinciple may be expressed more simply as taking a less favorable actionnow in order to produce higher reward options in the future. Thus, thedisclosed navigational system capable of long range planning may choosea suboptimal short term action where long term prediction indicates thata short term loss in reward may result in long term reward gains.

In general, autonomous driving applications may involve a series ofplanning problems, where the navigational system may decide on immediateactions in order to optimize a longer term objective. For example, whena vehicle is confronted with a merge situation at a roundabout, thenavigational system may decide on an immediate acceleration or brakingcommand in order to initiate navigation into the roundabout. While theimmediate action to the detected navigational state at the roundaboutmay involve an acceleration or braking command responsive to thedetected state, the long term objective is a successful merge, and thelong term effect of the selected command is the success/failure of themerge. The planning problem may be addressed by decomposing the probleminto two phases. First, supervised learning may be applied forpredicting the near future based on the present (assuming the predictorwill be differentiable with respect to the representation of thepresent). Second, a full trajectory of the agent may be modeled using arecurrent neural network, where unexplained factors are modeled as(additive) input nodes. This may allow solutions to the long-termplanning problem to be determined using supervised learning techniquesand direct optimization over the recurrent neural network. Such anapproach may also enable the learning of robust policies byincorporating adversarial elements to the environment.

Two of the most fundamental elements of autonomous driving systems aresensing and planning. Sensing deals with finding a compactrepresentation of the present state of the environment, while planningdeals with deciding on what actions to take so as to optimize-futureobjectives. Supervised machine learning techniques are useful forsolving sensing problems. Machine teaming algorithmic frameworks mayalso be used for the planning part, especially reinforcement learning(RL) frameworks, such as those described above.

RL may be performed in a sequence of consecutive rounds. At round 1, theplanner (a.k.a. the agent or driving policy module 803) may observe astate, s_(t)∈S, which represents the agent as well as the environment.It then should decide on an action a_(t)∈A. After performing the action,the agent receives an immediate reward, r_(l)∈

, and is moved to a new state. As an example, the host vehicle mayinclude an adaptive cruise control (ACC) system, in which the vehicleshould autonomously implement acceleration/braking so as to keep anadequate distance to a preceding vehicle while maintaining smoothdriving. The state can be modeled as a pair, s_(t)=(x_(t), v_(t))∈

², where x_(t) is the distance to the preceding vehicle and v_(t) is thevelocity of the host vehicle relative to the velocity of the precedingvehicle. The action a_(t)∈

will be the acceleration command (where the host vehicle slows down ifa_(t)<0). The reward can be a function that depends on |a_(t)|(reflecting the smoothness of driving) and on s_(t) (reflecting that thehost vehicle maintains a safe distance from the preceding vehicle). Thegoal of the planner is to maximize the cumulative reward (maybe up to atime horizon or a discounted sum of future rewards). To do so, theplanner may rely on a policy, π:S→A, which maps a state into art action.

Supervised Learning (SL) can be viewed as a special case of RL, in whichs, is sampled from some distribution over S, and the reward function mayhave the form r_(t)=−

(a_(t), y_(t)), where

is a loss function, and the learner observes the value of y_(t) which isthe (possibly noisy) value of the optimal action to take when viewingthe states s_(t). There may be several differences between a general RLmodel and a specific case of SL, and these differences can make thegeneral RL problem more challenging.

In some SL situations, the actions predictions) taken by the learner mayhave no effect on the environment. In other words, s_(t+1) and a, areindependent. This can have two important implications. First, in SL, asample (s₁, y₁), . . . , (s_(m), y_(m)) can be collected in advance, andonly then can the search begin fora policy (or predictor) that will havegood accuracy relative to the sample. In contrast, in RL, the states_(t+1) usually depends on the action taken (and also on the previousstate), which in turn depends on the policy used to generate the action.This ties the data generation process to the policy learning process.Second, because actions do not affect the environment in SL, thecontribution of the choice of a_(t) to the performance of π is local.Specifically, a_(t) only affects the value of the immediate reward. Incontrast, in RL, actions that are taken at round t might have along-term effect on the reward values in future rounds.

In SL, the knowledge of the “correct” answer, y_(i), together with theshape of the reward, r_(t)=−

(a_(t), y_(t)) may provide full knowledge of the reward for all possiblechoices of a_(t), which may enable calculation of the derivative of thereward with respect to a_(t). In contrast, in RL, a “one-shot” value ofthe reward may be all that can be observed for a specific choice ofaction taken. This may be referred to as a “bandit” feedback. This isone of the most significant reasons for the need of “exploration” as apart of long term navigational planning, because in RL-based systems, ifonly “bandit” feedback is available, the system may not always know ifthe action taken was the best action to take.

Many RL algorithms rely, at least in part, on the mathematically elegantmodel of a Markov Decision Process (MDP). The Markovian assumption isthat the distribution of s_(t+1) is fully determined given s_(t) anda_(t). This yields a closed form in expression for the cumulative rewardof a given policy in terms of the stationary distribution over states ofthe MOP. The stationary distribution of a policy can be expressed as asolution to a linear programming problem. This yields two families ofalgorithms: 1) optimization with respect to the primal problem, whichmay be referred to as policy search, and 2) optimization with respect toa dual problem, whose variables are called the value function, V^(π).The value function determines the expected cumulative reward if the MDPbegins from the initial state, s, and from there actions are chosenaccording to π. A related quantity is the state-action value function,Q^(π)(s, a), which determines the cumulative reward assuming a startfrom state, s, an immediately chosen action a, and from there on actionschosen according to π. The Q function may give rise to acharacterization of the optimal policy (using the Bellman's equation).In particular, the Q function may show that the optimal policy is adeterministic function from S to A (in fact, it may be characterized asa “greedy” policy with respect to the optimal Q function).

One potential advantage of the MDP model is that it allows coupling ofthe future into the present using the Q function. For example, giventhat a host vehicle is now in state, s, the value of Q^(π)(s, a) mayindicate the effect of performing action a on the future. Therefore, theQ function may provide a local measure of the quality of an action a,thus making the RL problem more similar to a SL scenario.

Many RL algorithms approximate the V function or the Q function in oneway or another. Value iteration algorithms, e.g., the Q learningalgorithm, may rely on the fact that the V and Q functions of theoptimal policy may be fixed points of some operators derived fromBellman's equation. Actor-critic policy iteration algorithms aim tolearn a policy in an iterative way, where at iteration t, the “critic”estimates Q^(π) ^(l) and based on this estimate, the “actor” improvesthe policy.

Despite the mathematical elegancy of MDPs and the convenience ofswitching to the Q function representation, this approach may haveseveral limitations. For example, an approximate notion of a Markovianbehaving state may be all that can be found in some cases. Furthermore,the transition of states may depend not only on the agent's action, butalso on actions of other players in the environment. For example, in theACC example mentioned above, while the dynamic of the autonomous vehiclemay be Markovian, the next state may depend on the behavior of thedriver of the other car, which is not necessarily Markovian, Onepossible solution to this problem is to use partially observed MDPs, inwhich it is assumed that there is a Markovian state, but an observationthat is distributed according to the hidden state is what can be seen.

A more direct approach may consider game theoretical generalizations ofMDPs (e.g., the Stochastic Games framework). Indeed, algorithms for MDPsmay be generalized to multi-agents games (e.g., minimax-Q learning orNash-Q learning). Other approaches may include explicit modeling of theother players and vanishing regret learning algorithms. Learning in amulti-agent setting may be more complex than in a single agent setting.

A second limitation or the Q function representation may arise bydeparting from a tabular setting. The tabular setting is when the numberof states and actions is small, and therefore, Q can be expressed as atable with |S| rows and |A| columns. However, if the naturalrepresentation of Sand A includes Euclidean spaces, and the state andaction spaces are discretized, the number of states/actions may beexponential in the dimension. In such cases, it may not be practical toemploy a tabular setting. Instead, the Q function may be approximated bysome function from a parametric hypothesis class (e.g., neural networksof a certain architecture). For example, a deep-Q-network (DQN) learningalgorithm may be used. In DQN, the state space can be continuous, butthe action space may remain a small discrete set. There may beapproaches for dealing with continuous action spaces, but they may relyon approximating the Q function. In any case, the Q function may becomplicated and sensitive to noise, and, therefore, may be challengingto learn.

A different approach may be to address the RL problem using a recurrentneural network (RNN). In some cases, RNN may be combined with thenotions of multi-agents games and robustness to adversarial environmentsfrom game theory. Further, this approach may be one that does notexplicitly rely on any Markovian assumption.

The following describes in more detail an approach for navigation byplanning based on prediction. In this approach, it may be assumed thatthe state space, S, is a subset of

, and the action space, A, is a subset

^(k). This may be a natural representation in many applications. Asnoted above, there may be two key differences between RL and SU: (1)because past actions affect future rewards, information from the futuremay need to be propagated back to the past; and (2) the “bandit” natureof rewards can blur the dependence between (state, action) and reward,which can complicate the learning process.

As a first step in the approach, an observation may be made that thereare interesting problems in which the bandit nature of rewards is not anissue. For example, reward value (as will be discussed in more detailbelow) for the ACC application may be differentiable with respect to thecurrent state and action. In fact, even if the reward is given in a“bandit” manner, the problem of learning a differentiable function,{circumflex over (r)}(s, a), such that {circumflex over (r)}(s_(t),a_(t))≈r_(l), may be a relatively straightforward SL problem (e.g., aone dimensional regression problem). Therefore, the first step of theapproach may be to either define the reward as a function, {circumflexover (r)}(s, a), which is differentiable with respect to s and a, or touse a regression learning algorithm in order to learn a differentiablefunction, {circumflex over (r)}, that minimizes at least some regressionloss over a sample with instance vector being (s_(t), a_(t))∈

^(d)×

^(k) and target scalar being r_(t). In some situations, in order tocreate a training set, elements of exploration may be used.

To address the connection between past and future, a similar idea may beused. For example, suppose a differentiable function {circumflex over(N)}(s, a) can be learned such that {circumflex over (N)}(s_(t),a_(t))≈s_(t+1). Learning such a function may be characterized as an SLproblem. {circumflex over (N)} may be viewed as a predictor for the nearfuture. Next, a policy that maps from S to A may be described using aparametric function π_(θ): S→A. Expressing π_(θ) as a neural network,may enable expression of an episode of running the agent for T roundsusing a recurrent neural network (RNN), where the next state is definedas s_(t+1)={circumflex over (N)}(s_(t), a_(t))+v_(t). Here, v_(t)

^(d) may be defined by the environment and may express unpredictableaspects of the near future. The fact that s_(t+1) depends on s_(t) anda_(t) in a differentiable manner may enable a connection between futurereward values and past actions. A parameter vector of the policyfunction, π_(θ), may be learned by back-propagation over the resultingRNN. Note that explicit probabilistic assumptions need not be imposed onv_(t). In particular, there need not be a requirement for a Markovianrelation. Instead, the recurrent network may be relied upon to propagate“enough” information between past and future. Intuitively, {circumflexover (N)}(s_(t), a_(t)) may describe the predictable part of the nearfuture, while v_(t) may express the unpredictable aspects, which mayarise due to the behavior of other players in the environment. Thelearning system should learn a policy that will be robust to thebehavior of other players. If ∥v_(t)∥ is large, the connection betweenpast actions and future reward values may be too noisy for learning ameaningful policy. Explicitly expressing the dynamic of the system in atransparent way may enable incorporation of prior knowledge more easily.For example, prior knowledge may simplify the problem of defining{circumflex over (N)}.

As discussed above, the learning system may benefit from robustnessrelative to an adversarial environment, such as the environment of ahost vehicle, which may include multiple other drivers that may act inunexpected way. In a model that does not impose probabilisticassumptions on environments may be considered in which v_(t) is chosenin an adversarial manner. In some cases, restrictions may be placed onμ_(t), otherwise the adversary can make the planning problem difficultor even impossible. One natural restriction may be to require that∥μ_(t)∥ is bounded by a constant.

Robustness against adversarial environments may be useful in autonomousdriving applications. Choosing μ_(t) in an adversarial way may evenspeed up the teaming process, as it can focus the learning system towarda robust optimal policy. A simple game may be used to illustrate thisconcept. The state is s_(t)∈

, the action is a_(t)∈

, and the immediate loss function is 0.1|a_(t)|+[|s_(t)|−2]₊, where[x]₊=max. {x, 0} is the ReLU (rectified linear unit) function. The nextstate is s_(t+1)=s_(t)+a_(t)+v_(t), where v_(t)∈[−0.5, 0.5] is chosenfor the environment in an adversarial manner. Here, the optimal policymay be written as a two layer network with ReLU:a_(t)=−[s_(t)−1.5]₊+|−s_(t)−1.5]₊. Observe that when |s_(t)|∈(1.5, 2],the optimal action may have a larger immediate loss than the action a=0.Therefore, the system may plan for the future and may not rely solely onthe immediate loss. Observe that the derivative of the loss with respectto a_(t) is 0.1 sign(a_(t)), and the derivative with respect to s_(t) is1[|s_(t)|>2] sign(s_(t)). In a situation in which s_(t)∈(1.5, 2], theadversarial choice of v_(t) would be to set v_(t)=0.5 and, therefore,there may be a non-zero loss on round t+1, whenever a_(L)>1.5−s_(t). Insuch cases, the derivative of the loss may back-propagate directly toa_(t). Thus, the adversarial choice of v_(t) may help the navigationalsystem obtain a non-zero back-propagation message in cases for which thechoice of a_(t) is sub-optimal. Such a relationship may aid thenavigational system in selecting present actions based on an expectationthat such a present action (even if that action would result in asuboptimal reward or even a loss) will provide opportunities in thefuture for more optimal actions that result in higher rewards.

Such an approach may be applied to virtually any navigational situationthat may arise. The following describes the approach applied to oneexample: adaptive cruise control (ACC). In the ACC problem, the hostvehicle may attempt to maintain an adequate distance to a target vehicleahead (e.g., 1.5 seconds to the target car). Another goal may be todrive as smooth as possible while maintaining the desired gap. A modelrepresenting this situation may be defined as follows. The state spaceis

³, and the action space is

. The first coordinate of the state is the speed of the target car, thesecond coordinate is the speed of the host vehicle, and the lastcoordinate is the distance between the host vehicle and target vehicle(e.g., location of the host vehicle minus the location of the targetalong the road curve). The action to be taken by the host vehicle is theacceleration, and may be denoted by a_(t). The quantity τ may denote thedifference in time between consecutive rounds. While τ may be set to anysuitable quantity, in one example, τ may be 0.1 seconds. Position,s_(t), may be denoted as s_(t)=(v_(t) ^(host), v_(t) ^(host), x_(t)),and the (unknown) acceleration of the target vehicle may be denoted asa_(t) ^(target).

The full dynamics of the system can be described by:

v _(t) ^(target)=[v _(t−1) ^(target) +τa _(t−1) ^(target)]⁻.

v _(t) ^(host)=[v _(t−1) ^(host) +τa _(t−1)]₊.

x _(t)=[x _(t−1) +r(v _(t−1) ^(target) −v _(t−1) ^(host))]₊

This can be described as a sum of two vectors:

$\begin{matrix}{s_{t} = \left( {\left\lbrack {{s_{t - 1}\lbrack 0\rbrack} + {\tau \; a_{t - 1}^{target}}} \right\rbrack_{+},\left\lbrack {{s_{t - 1}\lbrack 1\rbrack} + \; {\tau \; a_{t - 1}}} \right\rbrack_{+},\left\lbrack {{s_{t - 1}\lbrack 2\rbrack} + {\tau \left( {{s_{t - 1}\lbrack 0\rbrack} - {s_{t - 1}\lbrack 1\rbrack}} \right)}_{+}} \right)} \right.} \\{= {\underset{\underset{\hat{N}{({s_{t - 1},a_{t}})}}{}}{\left( {{s_{t - 1}\lbrack 0\rbrack},\left\lbrack {{s_{t - 1}\lbrack 1\rbrack} + {\tau \; a_{t - 1}}} \right\rbrack_{+},\left\lbrack {{s_{t - 1}\lbrack 2\rbrack} + {\tau \left( {{s_{t - 1}\lbrack 0\rbrack} - {s_{t - 1}\lbrack 1\rbrack}} \right)}} \right\rbrack_{+}} \right)} +}} \\{{\underset{\underset{v_{t}}{}}{\left( {{\left\lbrack {{s_{t - 1}\lbrack 0\rbrack} + {\tau \; a_{t - 1}^{target}}} \right\rbrack_{+} - {s_{t - 1}\lbrack 0\rbrack}},0,0} \right)}.}}\end{matrix}$

The first vector is the predictable part, and the second vector is theunpredictable part. The reward on round t is defined as follows:

−r _(t)=0.1 |a _(t)|+[|x _(t) /x* _(t)−1|−0.3]₊ where x* _(t)=max{1,1.5v_(t) ^(host)}

The first term may result in a penalty for non-zero accelerations, thusencouraging smooth driving. The second term depends on the ratio betweenthe distance to the target car, x_(t), and the desired distance, x*_(t)which is defined as the maximum between a distance of 1 meter and breakdistance of 1.5 seconds. In some cases, this ratio may be exactly 1, butas long as this ratio is within [0.7, 1.3], the policy may forego anypenalties, which may allow the host vehicle some slack in navigationcharacteristic that may be important in achieving a smooth drive.

Implementing the approach outlined above, the navigation system of thehost vehicle (e.g., through operation of driving policy module 803within processing unit 110 of the navigation system) may select anaction in response to an observed state. The selected action may bebased on analysis not only of rewards associated with the responsiveactions available relative to a sensed navigational state, but may alsobe based on consideration and analysis of future states, potentialactions in response to the futures states, and rewards associated withthe potential actions.

FIG. 16 illustrates an algorithmic approach to navigation based ondetection and long range planning. For example, at step 1601, the atleast one processing device 110 of the navigation system for the hostvehicle may receive a plurality of images. These images may capturescenes representative of an environment of the host vehicle and may besupplied by any of the image capture devices (e.g., cameras, sensors,etc.) described above. Analysis of one or more of these images at step1603 may enable the at least one processing device 110 to identify apresent navigational state associated with the host vehicle (asdescribed above).

At steps 1605, 1607, and 1609, various potential navigational actionsresponsive to the sensed navigational state may be determined. Thesepotential navigational actions (e.g., a first navigational actionthrough an N^(th) available navigational action) may be determined basedon the sensed state and the long range goals of the navigational system(e.g., to complete a merge, follow a lead vehicle smoothly, pass atarget vehicle, avoid an object in the roadway, slow for a detected stopsign, avoid a target vehicle cutting in, or any other navigationalaction that may advance the navigational goals of the system).

For each of the determined potential navigational actions, the systemmay determine an expected reward. The expected reward may be determinedaccording to any of the techniques described above and may includeanalysis of a particular potential action relative to one or more rewardfunctions. Expected rewards 1606, 1608, and 1610 may be determined foreach of the potential navigational actions (e.g., the first, second, andN^(th)) determined in steps 1605, 1607, and 1609, respectively.

In some cases, the navigational system of the host vehicle may selectfrom among the available potential actions based on values associatedwith expected rewards 1606, 1608, and 1610 (or any other type ofindicator of an expected reward). For example, in some situations, theaction that yields the highest expected reward may be selected.

In other cases, especially where the navigation system engages in longrange planning to determine navigational actions for the host vehicle,the system may not choose the potential action that yields the highestexpected reward. Rather, the system may look to the future to analyzewhether there may be opportunities for realizing higher rewards later iflower reward actions are selected in response to a current navigationalstate. For example, for any or all of the potential actions determinedat steps 1605, 1607, and 1609, a future state may be determined. Eachfuture state, determined at steps 1613, 1615, and 1617, may represent afuture navigational state expected to result based on the currentnavigational state as modified by a respective potential action (e.g.,the potential actions determined at steps 1605, 1607, and 1609).

For each of the future states predicted at steps 1613, 1615, and 1617,one or more future actions (as navigational options available inresponse to determined future state) may be determined and evaluated. Atsteps 1619, 1621, and 1623, for example, values or any other type ofindicator of expected rewards associated with one or more of the futureactions may be developed (e.g., based on one or more reward functions).The expected rewards associated with the one or more future actions maybe evaluated by comparing values of reward functions associated witheach future action or by comparing any other indicators associated withthe expected rewards.

At step 1625, the navigational system for the host vehicle may select anavigational action for the host vehicle based on a comparison ofexpected rewards, not just based on the potential actions identifiedrelative to a current navigational state (e.g., at steps 1605, 1607, and1609), but also based on expected rewards determined as a result ofpotential future actions available in response to predicted futurestates (e.g., determined at steps 1613, 1615, and 1617). The selectionat step 1625 may be based on the options and rewards analysis performedat steps 1619, 1621, and 1623.

The selection of a navigational action at step 1625 may be based on acomparison of expected rewards associated with future action optionsonly. In such a case, the navigational system may select an action tothe current state based solely on a comparison of expected rewardsresulting from actions to potential future navigational states. Forexample, the system may select the potential action identified at step1605; 1607, or 1609 that is associated with a highest future rewardvalue as determined through analysis at steps 1619, 1621, and 1623.

The selection of a navigational action at step 1625 may also be based oncomparison of current action options only (as noted above). In thissituation, the navigational system may select the potential actionidentified at step 1605, 1607, or 1609 that is associated with a highestexpected reward, 1606, 1608, or 1610. Such a selection may be performedwith little or no consideration of future navigational states or futureexpected rewards to navigational actions available in response toexpected future navigational states.

On the other hand, in some cases, the selection of a navigational actionat step 1625 may be based on a comparison of expected rewards associatedwith both future action options and with current action options. This,in fact, may be one of the principles of navigation based on long rangeplanning. For example, expected rewards to future actions may beanalyzed to determine if any may warrant a selection of a lower rewardaction in response to the current navigational state in order to achievea potential higher reward in response to a subsequent navigationalaction expected to be available in response to future navigationalstates. As an example, a value or other indicator of an expected reward1606 may indicate a highest expected reward from among rewards 1606,1608, and 1610. On the other hand, expected reward 1608 may indicate alowest expected reward from among rewards 1606, 1608, and 1610. Ratherthan simply selecting the potential action determined at step 1605(i.e., the action giving rise to the highest expected reward 1606),analysis of future states, potential future actions, and future rewardsmay be used in making a navigational action selection at step 1625. Inone example, it may be determined that a reward identified at step 1621(in response to at least one future action to a future state determinedat step 1615 based on the second potential action determined at step1607) may be higher than expected reward 1606. Based on this comparison,the second potential action determined at step 1607 may be selectedrather than the first potential action determined at step 1605 despiteexpected reward 1606 being higher than expected reward 1608. In oneexample, the potential navigational action determined at step 1605 mayinclude a merge in front of a detected target vehicle, while thepotential navigational action determined at step 1607 may include amerge behind the target vehicle. While the expected reward 1606 ofmerging in front of the target vehicle may be higher than the expectedreward 1608 associated with merging behind the target vehicle, it may bedetermined that merging behind the target vehicle may result in a futurestate for which there may be action options yielding even higherpotential rewards than expected reward 1606, 1608. or other rewardsbased on available actions in response to a current, sensed navigationalstate.

Selection from among potential actions at step 1625 may be based on anysuitable comparison of expected rewards (or any other metric orindicator of benefits associated with one potential action overanother). In some cases, as described above, a second potential actionmay be selected over a first potential action if the second potentialaction is projected to provide at least one Future action associatedwith an expected reward higher than a reward associated with the firstpotential action. In other cases, more complex comparisons may beemployed. For example, rewards associated with action options inresponse to projected future states may be compared to more than oneexpected reward associated with a determined potential action.

In some scenarios, actions and expected rewards based on projectedfuture states may affect selection of a potential action to a currentstate if at least one of the future actions is expected to yield areward higher than any of the rewards expected as a result of thepotential actions to a current state (e.g., expected rewards 1606, 1608,1610, etc.). In some cases, the future action option that yields thehighest expected reward (e.g., from among the expected rewardsassociated with potential actions to a sensed current state as well asfrom among expected rewards associated with potential future actionoptions relative to potential future navigational states) may be used asa guide for selection of a potential action to a current navigationalstate. That is, after identifying a future action option yielding thehighest expected reward (or a reward above a predetermined threshold,etc.), the potential action that would lead to the future stateassociated with the identified future action yielding the highestexpected reward may be selected at step 1625.

In other cases, selection of available actions may be made based ondetermined differences between expected rewards. For example, a secondpotential action determined at step 1607 may be selected if a differencebetween art expected reward associated with a future action determinedat step 1621 and expected reward 1606 is greater than a differencebetween expected reward 1608 and expected reward 1606 (assuming+signdifferences). In another example, a second potential action determinedat step 1607 may be selected if a difference between an expected rewardassociated with a future action determined at step 1621 and an expectedreward associated with a future action determined at step 1619 isgreater than a difference between expected reward 1608 and expectedreward 1606.

Several examples have been described for selecting from among potentialactions to a current navigational state. Any other suitable comparisontechnique or criteria, however, may be used for selecting an availableaction through long range planning based on action and reward analysisextending to projected future states. Additionally, while FIG. 16represents two layers in the long range planning analysis (e.g., a firstlayer considering the rewards resulting from potential actions to acurrent state, and a second layer considering the rewards resulting fromfuture action options in response to projected figure states), analysisbased on more layers may be possible. For example, rather than basingthe long range planning analysis upon one or two layers, three, four ormore layers of analysis could be used in selecting from among availablepotential actions in response to a current navigational state.

After a selection is made from among potential actions in response to asensed navigational state, at step 1627, the at least one processor maycause at least one adjustment of a navigational actuator of the hostvehicle in response to the selected potential navigational action. Thenavigational actuator may include any suitable device for controlling atleast one aspect of the host vehicle. For example, the navigationalactuator may include at least one of a steering mechanism, a brake, oran accelerator.

Navigation Based on Inferred Aggression of Others

Target vehicles may be monitored through analysis of an acquired imagestream to determine indicators of driving aggression. Aggression isdescribed herein as a qualitative or quantitative parameter, but othercharacteristics may be used: perceived level of attention (potentialimpairment of driver, distracted—cell phone, asleep, etc.). In somecases, a target vehicle may be deemed to have a defensive posture, andin some cases, the target vehicle may be determined to have a moreaggressive posture. Navigational actions may be selected or developedbased on indicators of aggression. For example, in some cases, therelative velocity, relative acceleration, increases in relativeacceleration, following distance, etc., relative to a host vehicle maybe tracked to determine lithe target vehicle is aggressive or defensive.If the target vehicle is determined to have a level of aggressionexceeding a threshold, for example, the host vehicle may be inclined togive way to the target vehicle. A level of aggression of the targetvehicle may also be discerned based on a determined behavior of thetarget vehicle relative to one or more obstacles in a path of or in avicinity of the target vehicle (e.g., a leading vehicle, obstacle in theroad, traffic light, etc.).

As an introduction to this concept, an example experiment will bedescribed with respect to a merger of the host vehicle into aroundabout, in which a navigational goal is to pass through and out ofthe roundabout. The situation may begin with the host vehicle approachesan entrance of the roundabout and may end with the host vehicle reachesan exit of the roundabout (e.g., the second exit). Success may bemeasured based on whether the host vehicle maintains a safe distancefrom all other vehicles at all times, whether the host vehicle finishesthe route as quickly as possible, and whether the host vehicle adheresto a smooth acceleration policy. In this illustration, N_(r) targetvehicles may be placed at random on the roundabout. To model a blend ofadversarial and typical behavior, with probability p, a target vehiclemay be modeled by an “aggressive” driving policy, such that theaggressive target vehicle accelerates when the host vehicle attempts tomerge in front of the target vehicle. With probability 1−p, the targetvehicle may be modeled by a “defensive” driving policy, such that thetarget vehicle decelerates and lets the host vehicle merge in. In thisexperiment, p=0.5, and the navigation system of the host vehicle may beprovided with no information about the type of the other drivers. Thetypes of other drivers may be chosen at random at the beginning of theepisode.

The navigational state may be represented as the velocity and locationof the host vehicle (the agent), and the locations, velocities, andaccelerations of the target vehicles. Maintaining target accelerationobservations may be important in order to differentiate betweenaggressive and defensive drivers based on the current state. All targetvehicles may move on a one-dimensional curve that outlines theroundabout path. The host vehicle may move on its own one-dimensionalcurve, which intersects the target vehicles' curve at the merging point,and this point is the origin of both curves. To model reasonabledriving, the absolute value of all vehicles' accelerations may be upperbounded by a constant. Velocities may also be passed through a ReLUbecause driving backward is not allowed. Note that by not allowingdriving backwards, long-term planning may become a necessity, as theagent cannot regret on its past actions.

As described above, the next state, s_(t+1), may be decomposed into asum of a predictable part, {circumflex over (N)}(s_(t), a_(t)), and anon-predictable part, v_(t). The expression, {circumflex over(N)}(s_(t), a_(t)), may represent the dynamics of vehicle locations andvelocities (which may be well-defined in a differentiable manner), whilev_(t) may represent the target vehicles' acceleration. It may beverified that {circumflex over (N)}(s_(t), a_(t)) can be expressed as acombination of ReLU functions over an affine transformation, hence it isdifferentiable with respect to s_(t) and a_(t). The vector v_(t) may bedefined by a simulator in a non-differentiable manner, and may implementaggressive behavior for some targets and defensive behavior for othertargets. Two frames from such a simulator are shown in FIGS. 17A and17B. In this example experiment, a host vehicle 1701 learned to slowdownas it approached the entrance of the roundabout. It also learned to giveway to aggressive vehicles (e.g., vehicles 1703 and 1705), and to safelycontinue when merging in front of defensive vehicles (e.g., vehicles1706, 1708, and 1710). In the example represented by FIGS. 17A and 17B,the navigation system of host vehicle 1701 is not provided with the typeof target vehicles. Rather, whether a particular vehicle is determinedto be aggressive or defensive is determined through inference based onobserved position and acceleration, for example, of the target vehicles.In FIG. 17A, based on position, velocity, and/or relative acceleration,host vehicle 1701 may determine that vehicle 1703 has an aggressivetendency and, therefore, host vehicle 1701 may stop and wait for targetvehicle 1703 to pass rather than attempting to merge in front of targetvehicle 1703. In FIG. 17B, however, target vehicle 1701 recognized thatthe target vehicle 1710 traveling behind vehicle 1703 exhibiteddefensive tendencies (again, based on observed position, velocity,and/or relative acceleration of vehicle 1710) and, therefore, completeda successful merge in front of target vehicle 1710 and behind targetvehicle 1703.

FIG. 18 provides a flowchart representing an example algorithm fornavigating a host vehicle based on predicted aggression of othervehicles. In the example of FIG. 18, a level of aggression associatedwith at least one target vehicle may be inferred based on observedbehavior of the target 31) vehicle relative to an object in theenvironment of the target vehicle. For example, at step 1801, at leastone processing device (e.g., processing device 110) of the host vehiclenavigation system may receive, from a camera associated with the hostvehicle, a plurality of images representative of an environment of thehost vehicle. At step 1803, analysis of one or more of the receivedimages may enable the at least one processor to identify a targetvehicle (e.g., vehicle 1703) in the environment of the host vehicle1701. At step 1805, analysis of one or more of the received images mayenable the at least one processing device to identify in the environmentof the host vehicle at least one obstacle to the target vehicle. Theobject may include debris in a roadway, a stoplight/traffic light, apedestrian, another vehicle (e.g., a vehicle traveling ahead of thetarget vehicle, a parked vehicle, etc.), a box in the roadway, a roadbarrier, a curb, or any other type of object that may be encountered inan environment of the host vehicle. At step 1807, analysis of one ormore or the received images may enable the at least one processingdevice to determine at least one navigational characteristic of thetarget vehicle relative to the at least one identified obstacle to thetarget vehicle.

Various navigational characteristics may be used to infer a level ofaggression of a detected target vehicle in order to develop anappropriate navigational response to the target vehicle. For example,such navigational characteristics may include a relative accelerationbetween the target vehicle and the at least one identified obstacle, adistance of the target vehicle from the obstacle (e.g., a followingdistance of the target vehicle behind another vehicle), and/or arelative velocity between the target vehicle and the obstacle, etc.

In some embodiments, the navigational characteristics of the targetvehicles may be determined based on outputs from sensors associated withthe host vehicle (e.g., radar, speed sensors, GPS, etc.). In some cases,however, the navigational characteristics of the target vehicles may bedetermined partially or fully based on analysis of images of anenvironment of the host vehicle. For example, image analysis techniquesdescribed above and in, for example, U.S. Pat. No. 9,168,868, which isincorporated herein by reference, may be used to recognize targetvehicles within an environment of the host vehicle. And, monitoring alocation of a target vehicle in the captured images over lime and/ormonitoring locations in the captured images of one or more featuresassociated with the target vehicle (e.g., tail lights, head lights,bumper, wheels, etc.) may enable a determination of relative distances,velocities, and/or accelerations between the target vehicles and thehost vehicle or between the target vehicles and one or more otherobjects in an environment of the host vehicle.

An aggression level of an identified target vehicle may be inferred fromany suitable observed navigational characteristic of the target vehicleor any combination of observed navigational characteristic-s. Forexample, a determination of aggressiveness may be made based on anyobserved characteristic and one or more predetermined threshold levelsor any other suitable qualitative or quantitative analysis. In someembodiments, a target vehicle may be deemed as aggressive if the targetvehicle is observed to be following the host vehicle or another vehicleat a distance less than a predetermined aggressive distance threshold.On the other hand, a target vehicle observed to be following the hostvehicle or another vehicle at a distance greater than a predetermineddefensive distance threshold may be deemed defensive. The predeterminedaggressive distance threshold need not be the same as the predetermineddefensive distance threshold. Additionally, either or both of thepredetermined aggressive distance threshold and the predetermineddefensive distance threshold may include a range of values, rather thana bright line value. Further, neither of the predetermined aggressivedistance threshold nor the predetermined defensive distance thresholdmust be fixed. Rather these values, or ranges of values, may shill overtime, and different thresholds/ranges of threshold values may be appliedbased on observed characteristics of a target vehicle. For example, thethresholds applied may depend on one or more other characteristics ofthe target vehicle. Higher observed relative velocities and/oraccelerations may warrant application of larger threshold values/ranges.Conversely, lower relative velocities and/or accelerations, includingzero relative velocities and/or accelerations, may warrant applicationof smaller distance threshold values/ranges in making dieaggressive/defensive inference.

The aggressive/defensive inference may also be based on relativevelocity and/or relative acceleration thresholds. A target vehicle maybe deemed aggressive if its observed relative velocity and/or itsrelative acceleration with respect to another vehicle exceeds apredetermined level or range. A target vehicle may be deemed defensiveif its observed relative velocity and/or its relative acceleration withrespect to another vehicle falls below a predetermined level or range.

While the aggressive/defensive determination may be made based on anyobserved navigational characteristic alone, the determination may alsodepend on any combination of observed characteristics. For example, asnoted above, in some cases, a target vehicle may be deemed aggressivebased solely on an observation that it is following another vehicle at adistance below a certain threshold or range. In other cases, however,the target vehicle may be deemed aggressive if it both follows anothervehicle at less than a predetermined amount (which may be the same as ordifferent than the threshold applied where the determination is based ondistance alone) and has a relative velocity and/or a relativeacceleration of greater than a predetermined amount or range. Similarly,a target vehicle may be deemed defensive based solely on an observationthat it is following another vehicle at a distance greater than acertain threshold or range. In other cases, however, the target vehiclemay be deemed defensive if it both follows another vehicle at greaterthan a predetermined amount (which may be the same as or different thanthe threshold applied where the determination is based on distancealone) and has a relative velocity and/or a relative acceleration ofless than a predetermined amount or range. System 100 may make anaggressive/defensive if, for example, a vehicle exceeds 0.5 Gacceleration or deceleration (e.g., jerk 5 m/s3), a vehicle has alateral acceleration of 0.5 G in a lane change or on a curve, a vehiclecauses another vehicle to do any of the above, a vehicle changes lanesand causes another vehicle to give way by more than 0.3 G decelerationor jerk of 3 m/s3, and/or a vehicle changes two lanes without stopping.

It should be understood that references to a quantity exceeding a rangemay indicate that the quantity either exceeds all values associated withthe range or falls within the range. Similarly, references to a quantityfalling below a range may indicate that the quantity either falls belowall values associated with the range or falls within the range.Additionally, while the examples described for making anaggressive/defensive inference are described with respect to distance,relative acceleration, and relative velocity, any other suitablequantities may be used. For example, a time to collision may calculationmay be used or any indirect indicator of distance, acceleration, and/orvelocity of the target vehicle. It should also be noted that while theexamples above focus on target vehicles relative to other vehicles, theaggressive/defensive inference may be made by observing the navigationalcharacteristics of a target vehicle relative to any other type ofobstacle (e.g., a pedestrian, road barrier, traffic light, debris,etc.).

Returning to the example shown in FIGS. 17A and 17B, as host vehicle1701 approaches the roundabout, the navigation system, including its atleast one processing device, may receive a stream of images from acamera associated with the host vehicle. Based on analysis of one ormore of the received images, any of target vehicles 1703, 1705, 1706,1708, and 1710 may be identified. Further, the navigation system mayanalyze the navigational characteristics of one or more of theidentified target vehicles. The navigation system nay recognize that thegap between target vehicles 1703 and 1705 represents the firstopportunity for a potential merge into the roundabout. The navigationsystem may analyze target vehicle 1703 to determine indicators ofaggression associated with target vehicle 1703. If target vehicle 1703is deemed aggressive, then the host vehicle navigation system may chooseto give way to vehicle 1703 rather than merging in front of vehicle1703. On the other hand, if target vehicle 1703 is deemed defensive,then the host vehicle navigation system may attempt to complete a mergeaction ahead of vehicle 1703.

As host vehicle 1701 approaches the roundabout, the at least oneprocessing device of the navigation system may analyze the capturedimages to determine navigational characteristics associated with targetvehicle 1703. For example, based on the images, it may be determinedthat vehicle 1703 is following vehicle 1705 at a distance that providesa sufficient gap for the host vehicle 1701 to safely enter. Indeed, itmay be determined that vehicle 1703 is following vehicle 1705 by adistance that exceeds an aggressive distance threshold, and therefore,based on this information, the host vehicle navigation system may beinclined to identify target vehicle 1703 as defensive. In somesituations, however, more than one navigational characteristic of atarget vehicle may be analyzed in making the aggressive/defensivedetermination, as discussed above. Furthering the analysis, the hostvehicle navigation system may determine that, while target vehicle 1703is following at a non-aggressive distance behind target vehicle 1705,vehicle 1703 has a relative velocity and/or a relative acceleration withrespect to vehicle 1705 that exceeds one or more thresholds associatedwith aggressive behavior. Indeed, host vehicle 1701 may determine thattarget vehicle 1703 is accelerating relative to vehicle 1705 and closingthe gap that exists between vehicles 1703 and 1705. Based on furtheranalysis of the relative velocity, acceleration, and distance (and evena rate that the gap between vehicles 1703 and 1705 is closing), hostvehicle 1701 may determine that target vehicle 1703 is behavingaggressively. Thus, while there may be a sufficient gap into which hostvehicle may safely navigate, host vehicle 1701 may expect that a mergein front of target vehicle 1703 would result in an aggressivelynavigating vehicle directly behind the host vehicle. Further, targetvehicle 1703 may be expected, based on the observed behavior throughimage analysis or other sensor output, that target vehicle 1703 wouldcontinue accelerating toward host vehicle 1701 or continuing toward hostvehicle 1701 at a non-zero relative velocity if host vehicle 1701 was tomerge in front of vehicle 1703. Such a situation may be undesirable froma safety perspective and may also result in discomfort to passengers ofthe host vehicle. For such reasons, host vehicle 1701 may choose to giveway to vehicle 1703, as shown in FIG. 17B, and merge into the roundaboutbehind vehicle 1703 and in front of vehicle 1710, deemed defensive basedon analysis of one or more of its navigational characteristics.

Returning to FIG. 18, at step 1809, the at least one processing deviceof the navigation system of the host vehicle may determine, based on theidentified at least one navigational characteristic of the targetvehicle relative to the identified obstacle, a navigational action forthe host vehicle (e.g., merge in front of vehicle 1710 and behindvehicle 1703). To implement the navigational action (at step 1811), theat least one processing device may cause at least one adjustment of anavigational actuator of the host vehicle in response to the determinednavigational action. For example, a brake may be applied in order togive way to vehicle 1703 in FIG. 17A, and an accelerator may be appliedalong with steering of the wheels of the host vehicle in order to causethe host vehicle to enter the roundabout behind vehicle 1703, as shownif FIG. 17B.

As described in the examples above, navigation of the host vehicle maybe based on the navigational characteristics of a target vehiclerelative to another vehicle or object. Additionally, navigation of thehost vehicle may be based on navigational characteristics of the targetvehicle alone without a particular reference to another vehicle orobject. For example, at step 1807 of FIG. 18, analysis of a plurality ofimages captured from an environment of a host vehicle may enabledetermination of at least one navigational characteristic of anidentified target vehicle indicative of a level of aggression associatedwith the target vehicle. The navigational characteristic may include avelocity, acceleration, etc. that need not be referenced with respect toanother object or target vehicle in order to make anaggressive/defensive determination. For example, observed accelerationsand/or velocities associated with a target vehicle that exceed apredetermined threshold or fall within or exceed a range of values mayindicate aggressive behavior. Conversely, observed accelerations and/orvelocities associated with a target vehicle that fall below apredetermined threshold or fall within or exceed a range of values mayindicate defensive behavior.

Of course, in some instances the observed navigational characteristic(e.g., a location, distance, acceleration, etc. may be referencedrelative to the host vehicle in order to make the aggressive/defensivedetermination. For example, an observed navigational characteristic ofthe target vehicle indicative of a level of aggression associated withthe target vehicle may include an increase in relative accelerationbetween the target vehicle and the host vehicle, a following distance ofthe target vehicle behind the host vehicle, a relative velocity betweenthe target vehicle and the host vehicle, etc.

Navigation Based on Accident Liability Constraint

As described in the sections above, planned navigational actions may betested against predetermined constraints to ensure compliance withcertain rules. In some embodiments, this concept may be extended toconsiderations of potential accident liability. As discussed below, aprimary goal of autonomous navigation is safety. As absolute safety maybe impossible (e.g., at least because a particular host vehicle underautonomous control cannot control the other vehicles in itssurroundings—it can only control its own actions), the use of potentialaccident liability as a consideration in autonomous navigation and,indeed, as a constraint to planned actions may help ensure that aparticular autonomous vehicle does not take any actions that are deemedunsafe—e.g., those for which potential accident liability may attach tothe host vehicle. If the host vehicle takes only actions that are safeand that are determined not to result in an accident of the hostvehicle's own fault or responsibility, then desired levels of accidentavoidance (e.g., fewer than 10⁻⁹ per hour of driving) may be achieved.

The challenges posed by most current approaches to autonomous drivinginclude a lack of safety guarantees (or at least an inability to providedesired levels of safety), and also a lack of scalability. Consider theissue of guaranteeing multi-agent safe driving. As society will unlikelytolerate road accident fatalities caused by machines, an acceptablelevel of safety is paramount to the acceptance of autonomous vehicles.While a goal may be to provide zero accidents, this may be impossiblesince multiple agents are typically involved in an accident and one mayenvision situations where an accident occurs solely due to the blame ofother agents. For example, as shown in FIG. 19, host vehicle 1901 driveson a multi-lane highway, and while host vehicle 1901 can control its ownactions relative to the target vehicles 1903, 1905, 1907, and 1909, itcannot control the actions of the target vehicles surrounding it. As aresult, host vehicle 1901 may be unable to avoid an accident with atleast one of the target vehicles should vehicle 1905, for example,suddenly cut in to the host vehicle's lane on a collision course withthe host vehicle. To address this difficulty, a typical response ofautonomous vehicle practitioners is to resort to a statisticaldata-driven approach where safety validation becomes tighter as dataover more mileage is collected.

To appreciate the problematic nature of a data-driven approach tosafety, however, consider first that the probability of a fatalitycaused by an accident per one hour of (human) driving is known to be10⁻⁶. It is reasonable to assume that for society to accept machines toreplace humans in the task of driving, the fatality rate should bereduced by three orders of magnitude, namely to a probability of 10⁻⁹per hour. This estimate is similar to the assumed fatality rate of airbags and from aviation standards. For example, 10⁻⁹ is the probabilitythat a wing will spontaneously detach from an aircraft in mid-air.Attempts to guarantee safety using a data-driven statistical approachthat provides additional confidence with accumulating miles driven,however, is not practical. The amount of data required to guarantee aprobability of 10⁻⁹ fatality per hour of driving is proportional to itsinverse (i.e., 10⁹ hours of data) which is roughly on the order ofthirty billion miles. Moreover, a multi-agent system interacts with itsenvironment and likely cannot be validated offline (unless a realisticsimulator emulating real human driving with all its richness andcomplexities such as reckless driving is available—but the problem ofvalidating the simulator would be even more difficult than creating asafe autonomous vehicle agent). And any change to the software ofplanning and control will require a new data collection of the samemagnitude, which is clearly unwieldy and impractical. Further,developing a system through data invariably suffers from lack ofinterpretability and explainability of the actions being taken—if anautonomous vehicle (AV) has an accident resulting in a fatality, we needto know the reason. Consequently, a model-based approach to safety isrequired, but the existing “functional safety” and ASIL requirements inthe automotive industry are not designed to cope with multi-agentenvironments.

A second primary challenge in developing a safe driving model forautonomous vehicles is the need for scalability. The premise underlyingAV goes beyond “building a better world” and instead is based on thepremise that mobility without a driver can be sustained at a lower costthan with a driver. This premise is invariably coupled with the notionof scalability—in the sense of supporting mass production of AVs (in themillions) and more importantly of supporting a negligible incrementalcost to enable driving in a new city. Therefore the cost of computingand sensing does matter, if AV is to be mass manufactured, the cost ofvalidation and the ability to drive “everywhere” rather than in a selectfew cities is also a necessary requirement to sustain a business.

The issue with most current approaches lies in a “brute force” state ofmind along three axes: (i) the required “computing density”, (ii) theway high-definition maps are defined and created, and (iii) the requiredspecification from sensors. A brute-force approach goes againstscalability and shifts the weight towards a future in which unlimitedon-board computing is ubiquitous, where the cost of building andmaintaining HD-naps becomes negligible and scalable, and exotic superadvanced sensors would be developed, productized to automotive grade,and at a negligible cost. A future for which any of the above comes tofruition is indeed plausible but having all of the above hold is likelya low-probability event. Thus, there is a need to provide a formal modelthat pieces together safety and scalability into an AV program thatsociety can accept and is scalable in the sense of supporting millionsof cars driving anywhere in the developed countries.

The disclosed embodiments represent a solution that may provide thetarget levels of safety (or may even surpass safety targets) and mayalso be scalable to systems including millions of autonomous vehicles(or more). On the safety front, a model called “Responsibility SensitiveSafety” (RSS) is introduced that formalizes the notion of “accidentblame,” is interpretable and explainable, and incorporates a sense of“responsibility” into the actions of a robotic agent. The definition ofRSS is agnostic to the manner in which it is implemented which is a keyfeature to facilitate a goal of creating a convincing global safetymodel. RSS is motivated by the observation (as in FIG. 19) that agentsplay a non-symmetrical role in an accident where typically only one ofthe agents is responsible for the accident and therefore is to beresponsible for it. The RSS model also includes a formal treatment of“cautious driving” under limited sensing conditions where not all agentsare always visible (due to occlusions, for example). One primary goal ofthe RSS model is to guarantee that an agent will never make an accidentof its “blame” or for which it is responsible. A model may be usefulonly if it comes with an efficient policy (e.g., a function that mapsthe “sensing state” to an action) that complies with RSS. For example,an action that appears innocent at the current moment might lead to acatastrophic event in the far future (“butterfly effect”). RSS may beuseful for constructing a set of local constraints on the short-termfuture that may guarantee (or at least virtually guarantee) that noaccidents will happen in the future as a result of the host vehicle'sactions.

Another contribution evolves around the introduction of a “semantic”language that consists of units, measurements, and action space, andspecification as to how they are incorporated into planning, sensing andactuation of the AV. To get a sense of semantics, in this context,consider how a human taking driving lessons is instructed to think abouta “driving policy.” These instructions are not geometric—they do nottake the form “drive 13.7 meters at the current speed and thenaccelerate at a rate of 0.8 m/s²”. Instead, the instructions are of asemantic nature “follow the car in front of you” or “overtake that caron your left.” The typical language of human driving policy is aboutlongitudinal and lateral goals rather than through geometric units ofacceleration vectors. A formal servant semantic language may be usefulon multiple fronts connected to the computational complexity of planningthat do not scale up exponentially with time and number of agents, tothe manner in which safety and comfort interact, to the way thecomputation of sensing is defined and the specification of sensormodalities and how they interact in a fusion methodology. A fusionmethodology (based on the semantic language) may ensure that the RSSmodel achieves the required 10⁻⁹ probability of fatality, per one hourof driving, all while performing only offline validation over a datasetof the order of 10⁵ hours of driving data.

For example, in a reinforcement learning setting, a Q function (e.g., afunction evaluating the long term quality of performing an action a c Awhen the agent is at state s r S; given such a Q-function, a naturalchoice of an action may be to pick the one with highest quality,π(s)=argmax_(a) Q(s, a)) may be defined over a semantic space in whichthe number of trajectories to be inspected at any given time is boundedby 10⁴ regardless of the time horizon used for planning. The signal tonoise ratio in this space may be high, allowing for effective machinelearning approaches to succeed in modeling the Q function. In the caseof computation of sensing, semantics may allow for distinguishingbetween mistakes that affect safety versus those mistakes that affectthe comfort of driving. We define a PAC model (Probably ApproximateCorrect (PAC)), borrowing Variants PAC-learning terminology) for sensingwhich is tied to the Q-function and show how measurement mistakes areincorporated into planning in a manner that complies with RSS yet allowsfor optimization of the comfort of driving. The language of semanticsmay be important for the success of certain aspects of this model asother standard measures of error, such as error with respect to a globalcoordinate system, may not comply with the PAC sensing model. Inaddition, the semantic language may be an important enabler for definingHD-maps that can be constructed using low-bandwidth sensing data andthus be constructed through crowd-sourcing and support scalability.

To summarize, the disclosed embodiments may include a formal model thatcovers important ingredients of an AV: sense, plan, and act. The modelmay help ensure that from a planning perspective there will be noaccident of the AV's own responsibility. And also through a PAC-sensingmodel, even with sensing errors, the described fusion methodology mayrequire only offline data collection of a very reasonable magnitude tocomply with the described safety model. Furthermore, the model may tietogether safety and scalability, through the language of semantics,thereby providing a complete methodology for a safe and scalable AV.Finally, it is worth noting that developing an accepted safety modelthat would be adopted by the industry and regulatory bodies may be anecessary condition for the success of AV.

The RSS model may generally follow a classic sense-plan-act roboticcontrol methodology. The sensing system may be responsible forunderstanding a present state of the environment of a host vehicle. Theplanning part, which may be referred to as a “driving policy” and whichmay be implemented by a set of hard-coded instructions, through atrained system (e.g., a neural network), or a combination, may beresponsible for determining what is the best next move in view ofavailable options for accomplishing a driving goal (e.g., how to movefrom the left lane to a right lane in order to exit a highway). Theacting portion is responsible for implementing the plan (e.g., thesystem of actuators and one or more controllers for steering,accelerating, and/or braking, etc. a vehicle in order to implement aselected navigational action). The described embodiments below focusprimarily on the sensing and planning parts.

Accidents may stem from sensing errors or planning errors. Planning is amulti-agent endeavor, as there are other road users (humans andmachines) that react to actions of an AV. The described RSS model isdesigned to address safety for the planning part, among others. This maybe referred to as multi-agent safety. In a statistical approach,estimation of the probability of planning errors may be done “online.”Namely, after every update of the software, billions of miles must bedriven with the new version to provide an acceptable level of estimationof the frequency of planning errors. This is clearly infeasible. As analternative, the RSS model may provide a 100% guarantee (or virtually100% guarantee) that the planning module will not make mistakes of theAV's blame (the notion of “blame” is formally defined). The RSS modelmay also provide an efficient means for its validation not reliant upononline testing.

Errors in a sensing system may be easier to validate, because sensingcan be independent of the vehicle actions, and therefore we can validatethe probability of a severe sensing error using “offline” data. But,even collecting offline data of more than 10⁹ hours of driving ischallenging. As part of the description of a disclosed sensing system, afusion approach is described that can be validated using a significantlysmaller amount of data.

The described RSS system may also be scalable to millions of cars. Forexample, the described semantic driving policy and applied safetyconstraints may be consistent with sensing and mapping requirements thatcan scale to millions of cars even in today's technology.

For a foundational building block of such a system is a thorough safetydefinition, that is, a minimal standard to which AV systems may need toabide. In the following technical lemma, a statistical approach tovalidation of an AV system is shown to be infeasible, even forvalidating a simple claim such as “the system makes N accidents perhour”. This implies that a model-based safety definition is the onlyfeasible tool for validating an AV system.

Lemma 1 Let X be a probability space, and A be an event far whichPr(A)=p₁<0.1. Assume we sample

$m = {\frac{1}{p_{1}}\mspace{14mu} {i.i.d.}}$

samples from X, and let Z=Σ_(t=1) ^(m) 1_([∈A]). Then

Pr(Z=0)≥e ⁻².

Proof We use the inequality 1−x≥e^(−2x) (proven for completeness inAppendix A.1), to get

Pr(Z=0)=(1−p ₁)^(m) ≥e ^(−2p) ¹ ^(m) =e ⁻².

Corollary 1 Assume an AV system AV₁ makes an accident with small yetinsufficient probability p_(t). Any deterministic validation procedurewhich is given samples, will, with constant probability, not distinguishbetween AV₁ and a different AV system AV₀ which never makes accidents.

To gain perspective over the typical values for such probabilities,assume we desire an accident probability of 10⁻⁹ per hour, and a certainAV system provides only 10⁻⁸ probability. Even if the system obtains 10⁸hours of driving, there is constant probability that the validationprocess will not be able to indicate that the system is dangerous.

Finally, note that this difficulty is for invalidating a single,specific, dangerous AV system. A full solution cannot be a viewed as asingle system, as new versions, bug fixes, and updates will benecessary. Each change, even of a single line of code, generates a newsystem front a validator's perspective. Thus, a solution which isvalidated statistically, must do so online, over new samples after everysmall fix or change, to account for the shift in the distribution ofstates observed and arrived-at by the new system. Repeatedly andsystematically obtaining such a huge number of samples (and even then,with constant probability, failing to validate the system), isinfeasible.

Further, any statistical claim must be formalized to be measured.Claiming a statistical property over the number of accidents a systemmakes is significantly weaker than claiming “it drives in a safemanner.” In order to say that, one must formally define what is safety.

Absolute Safety is Impossible

An action a taken by a car c may be deemed absolutely safe if noaccident can follow the action at some future time. It can be seen thatit is impossible to achieve absolute safety, by observing simple drivingscenarios, for example, as depicted in FIG. 19. From the perspective orvehicle 1901, no action can ensure that none of the surrounding carswill crash into it. Solving this problem by forbidding the autonomouscar from being in such situations is also impossible. As every highwaywith more than two lanes will lead to it at some point, forbidding thisscenario amounts to a requirement to remain in the garage. Theimplications might seem, at first glance, disappointing. Nothing isabsolutely safe. However, such a requirement for absolute safety, asdefined above, may be too harsh, as evident by the fact that humandrivers do not adhere to a requirement for absolute safety. Instead,humans behave according to a safety notion that depends onresponsibility.

Responsibility-Sensitive Safety

An important aspect missing from the absolute safety concept is thenon-symmetry of most accidents—it is usually one of the drivers who isresponsible for a crash, and is to be blamed. In the example of FIG. 19,the central car 1901 is not to be blamed if the left car 1909, forexample, suddenly drives into it. To formalize the fact that consideringits lack of responsibility, a behavior of AV 1901 staying in its ownlane can be considered safe. To do so, a formal concept of “accidentblame” or accident responsibility, which can serve as the premise for asafe driving approach, is described.

As an example, consider the simple case of two cars c_(f), c_(r),driving at the same speed, one behind the other, along a straight road.Assume c_(f), the car at the front, suddenly brakes because of anobstacle appearing on the road, and manages to avoid it. Unfortunately,c_(r) did not keep enough of a distance from c_(f), is not able torespond in time, and crashes into c_(f)'s rear side. It is clear thatthe blame is on c_(r); it is the responsibility of the rear car to keepsafe distance from the front car, and to be ready for unexpected, yetreasonable, braking,

Next, consider a much broader family of scenarios: driving in amulti-lane road, where cars can freely change lanes, cut into othercars' paths, drive at different speeds, and so on. To simplify thefollowing discussion, assume a straight road on a planar surface, wherethe lateral, longitudinal axes are the x, y axes, respectively. This canbe achieved, under mild conditions, by defining a homomorphism betweenthe actual curved road and a straight road. Additionally, consider adiscrete time space. Definitions may aid in distinction between twointuitively different sets of cases: simple ones, where no significantlateral maneuver is performed, and more complex ones, involving lateralmovement.

Definition 1 (Car Corridor) The corridor of a car c is the range[c_(x,left), c_(x,right)]×[±∞], where c_(x,left), c_(x,right) are thepositions of the leftmost, rightmost corners of c.

Definition 2 (Cut-in) A car c₁ (car 2003 in FIGS. 20A and 20B) cuts-into car c₀'s (car 2001 in FIGS. 20A and 20B) corridor at time it did notintersect c₀'s corridor at time t−1, and does intersect it at time t.

A further distinction may be made between front/back parts of thecorridor. The term “the direction of a cut-in” may describe movement inthe direction of the relevant corridor boundary. These definitions maydefine cases with lateral movement. For the simple case where there isno such occurrence, such as the simple case of a car following another,the safe longitudinal distance is defined:

Definition 3 (Safe longitudinal distance) A longitudinal distance 2101(FIG. 21) between a car c_(r) (car 2103) and another car c_(f) (car2105) that is in c_(r)'s frontal corridor is safe w.r.t. a response limep if for any braking command a, |a|<a_(max,brake), performed by c_(f),if c_(r) will apply its maximal brake f nom time p until a full stopthen it won't collide with c_(f).

Lemma 2 below calculates d as a function of the velocities of c_(r),c_(f), the response time ρ, and the maximal acceleration a_(max,brake).Both ρ and a_(max,brake) are constants, which should be determined tosome reasonable values by regulation.

Lemma 2 Let c_(r) be a vehicle which is behind c_(f) on the longitudinalaxis. Let a_(max,brake), and the maximal braking and accelerationcommands, and let ρ be c_(r)'s response time. Let v_(r), v_(f) be thelongitudinal velocities of the cars, and let l_(f), l_(r) be theirlengths. Define v_(p,max)=v_(r)+ρ·a_(max,accel), and define

$T_{r} = {{p + {\frac{v_{\rho,\max}}{a_{\max,{brake}}}\mspace{14mu} {and}\mspace{14mu} T_{j}}} = {\frac{v_{f}}{a_{\max,{brake}}}.}}$

Let L=(l_(r)+l_(f))/2. Then, the minimal sale longitudinal distance forc_(r) is:

$d_{\min} = \left\{ \begin{matrix}L & {{{if}\mspace{14mu} T_{r}} \leq T_{f}} \\{L + {T_{f}\left\lbrack {\left( {v_{\rho,\max} - v_{f}} \right) + {\rho \; a_{\max,{brake}}}} \right\rbrack} - \frac{\rho^{2}a_{\max,{brake}}}{2} +} & {otherwise} \\\frac{\left( {T_{r} - T_{f}} \right)\left( {v_{\rho,\max} - {\left( {T_{f} - \rho} \right)a_{\max,{brake}}}} \right)}{2} & \;\end{matrix} \right.$

Proof Let d_(t) be the distance at time t. To prevent an accident, wemust have that d_(t)<L for every t. To construct d_(min) we need to findthe tightest needed lower bound on d₀. Clearly, d₀ must be at least L.As long as the two cars didn't stop after T≥ρ seconds, the velocity ofthe preceding car will be v_(f)−T a_(max,brake) while c_(r)'s velocitywill be upper bounded by v_(ρ,max)−(T−ρ) a_(max,accel). So, the distancebetween the cars after T seconds will be lower bounded by:

$d_{T}:={d_{0} + {\frac{T}{2}\left( {{2v_{f}} - {T\mspace{11mu} a_{\max,{brake}}}} \right)} - {\quad{\left\lbrack {{\rho \; v_{\rho,\max}} + {\frac{T - \rho}{2}\left( {{2v_{\rho,\max}} - {\left( {T - \rho} \right)a_{\max,{brake}}}} \right)}} \right\rbrack = {d_{0} + {T\left\lbrack {\left( {v_{f} - v_{\rho,\max}} \right) - {\rho \; a_{\max,{brake}}}} \right\rbrack} + \frac{\rho^{2}a_{\max,{brake}}}{2}}}}}$

Note that T_(r) is the time on which c_(r) arrives to a full stop (avelocity of 0) and T_(f) is the time on which the other vehicle arrivesto a full stop. Note thata_(max,brake)(T_(r)−T_(f))=v_(p,max)−v_(f)+ρa_(max,brake), so ifT_(r)≤T_(f) it suffices to require that d₀>L. If T_(r)<T_(f) then

$d_{T_{r}} = {d_{0} + {T_{f}\left\lbrack {\left( {v_{f} - v_{\rho,\max}} \right) - {\rho \; a_{\max,{brake}}}} \right\rbrack} + \frac{\rho^{2}a_{\max,{brake}}}{2} - {\frac{\left( {T_{r} - T_{f}} \right)\left( {v_{\rho,\max} - {\left( {T_{f} - \rho} \right)a_{\max,{brake}}}} \right)}{2}.}}$

Requiring d_(Tr)>L and rearranging terms concludes the proof.

Finally, a comparison operator is defined which allows comparisons withsome notion of “margin”: when comparing lengths, velocities and so on,it is necessary to accept very similar quantities as “equal”.

Definition 4 (μ-comparison) The μ-comparison of two numbers a, b isa>_(μ)b if a>b+μ, a<_(μ)b if a<b−μ and a=_(μ)b if |a−b|≤μ.

The comparisons (argmin, argmax, etc.) below are μ-comparisons for somesuitable μs. Assume an accident occurred between cars c_(i), c₂. Toconsider who is to blame for the accident, the relevant moment whichneeds to be examined is defined. This is some point in time whichpreceded the accident, and intuitively, was the “point of no return”;after it, nothing could be done to prevent the accident.

Definition 5 (Blame Time) The Blame Time of an accident is the earliesttune preceding the accident in which:

there was an intersection between one of the cars and the other'scorridor, and

the longitudinal distance was not safe.

Clearly there is such a time, since at the moment of accident, bothconditions hold. Blame Times may be split into two separate categories:

-   -   Ones in which a cut-in also occurs, namely, they are the first        moment of intersection of one car and the other's corridor, and        it's in a non-safe distance.    -   Ones in which a cut-in does not occur, namely, there was        intersection with the corridor already, in a safe longitudinal        distance, and the distance had changed to unsafe at the Blame        Time.

Definition 6 (μ-Losing by Lateral Velocity) Assume a cut-in occursbetween cars c₁, c₂. We say that c₁ μ-Loses by Lateral Velocity in caseits lateral w.r.t. the direction of the cut-in is higher by μ than thatof c₂.

It should be noted that the direction of the velocity is important: Forexample, velocities of −1, 1 (both cars crashing into each other) is atie, however if the velocities are 1, 1+μ/2, the one with positivedirection towards the other car is to be blamed. Intuitively, thisdefinition will allow us to blame a car which drives laterally very fastinto another.

Definition 7 ((μ₁, μ₂)—Winning by Lateral Position) Assume a cut-inoccurs between cars c₁, c₂. We say that c₁ (μ₁, μ₂)—Wins by LateralPosition in case its lateral position w.r.t. the cut-in lane's center(the center closest to the cut-in relevant corridor) is smaller than μ₁(in absolute value), and smaller by μ₂ than that of c₂.

Intuitively, we will not blame a car if it's very close to the lanecenter (μ₁), and much closer than the other car (by μ₂).

Definition 8 (Blame) The Blaine or responsibility for an accidentbetween cars c₁, c₂, is a function of the stale at the Blame Time, andis defined as follows:

-   -   If the Blame Time is not a cut-in time, the blame is on the rear        car.

If the Blame Time is also a cut-in time, the blame is on both cars,unless for one of the cars, w.l.o.g. c₁, the two following conditionshold, for some predefined μs:

-   -   It doesn't lose by Lateral Velocity,    -   It wins by Lateral Position.

In that case, c1 is spared. In other words, if an unsafe cut-in occurs,both cars are to blame, unless one of the cars is not (significantly)laterally faster, and is (significantly) closer to the lane center. Bythis, the desired behavior is captured: if following a car, keep a safedistance, and if cutting into a corridor of a car which simply drives inits own lane, do it only at a safe distance. An automatedcontroller-based system for following the safety guidelines describedabove should not lead to overly defensive driving, as discussed furtherbelow.

Dealing with Limited Sensing

After considering the highway example, a second example next addresses aproblem of limited sensing. A very common human response, when blamedfor an accident, falls into the “but couldn't see him” category. It is,many times, true. Human sensing capabilities are limited, sometimesbecause of an unaware decision to focus on a different part of the road,sometimes because of carelessness, and sometimes because of physicallimitations—it is impossible to see a pedestrian hidden behind a parkedcar. Of those human limitations, advanced automatic sensing systems mayonly be subject to the latter: 360° view of the road, along with thefact that computers are never careless, puts them above human sensingcapabilities. Returning to the “but I couldn't see him” example, afitting answer is “well, you should've been more careful.” To formalizewhat is being careful with respect to limited sensing, consider thescenario, depicted in FIG. 22. Car 2201 (c₀) is trying to exit a parkinglot, merging into a (possibly) busy road, but cannot see whether thereare cars in the street because its view is obscured by building 2203.Assume that this is an urban, narrow street, with a speed Limit of 30km/h. A human driver's behavior is to slowly merge onto the road,obtaining more and more field of view, until sensing limitations areeliminated. A significant moment in time should be defined—the firsttime the occluded object is exposed to us; after its exposure, one dealwith it just like any other object that one can sense.

Definition 9 (Exposure Time) The Exposure Time ref an object is thefirst time in which we see it.

Definition 10 (Blame due to Unreasonable Speed) Assume that at theexposure time or after it, car c₁ (car 2205) was driving at speedv>v_(limit), and c₀ wasn't doing so. Then, the blame is only on c₁. Wesay that c₁ is blamed due to unreasonable speed.

This extension allows c₀ to exit the parking lot safely. Using ourprevious responsibility-sensitive safety definitions, along with adynamic v_(limit) definition (which uses the road conditions and speedlimit, plus reasonable margins), the only necessity is to check whetherin the worst case, as illustrated in the figure, the cut-in is in a safelongitudinal distance, while assuming that c₁ will not exceed v_(limit).Intuitively, this encourages c₀ to drive slower and further from theoccluder, thus slowly increasing its field of view and later allowingfor safe merging into the street.

Having extended the accident responsibility definition to this basiccase of limited sensing, a family of extensions may address similarcases. Simple assumptions as to what can be occluded (a potentially fastcar cannot be occluded between two closely parked cars, but a pedestriancan), and what is the worst case maneuver it can perform (a pedestrian'sv_(limit) is much smaller than that of a car), imply restrictions ondriving—one must be prepared for the worst, and have the ability torespond if suddenly, the exposure time comes. A more elaborate example,in an urban scenario, can be taken from the scenario of a pedestrianwhich is possibly occluded by a parked car. Accident blame for accidentswith a pedestrian may be defined:

Definition 11 (Accident-with-Pedestrian Blame) TheAccident-with-Pedestrian Blame is always on the car, unless one offollowing three holds:

-   -   the car hits the pedestrian with the car's side, and the lateral        velocity of the car is smaller than μ, w.r.t. the direction of        the hit.    -   the pedestrian's velocity at the exposure time or later was        larger than v_(limit).    -   the car is at complete stop.

Informally, the car is not to blame only if a pedestrian runs into itsside, while the car does not ride faster than μ into the pedestrian, orif the car is at stop, or if the pedestrian was running super-humanlyfast, in some direction, not necessarily the hitting direction.

While the described system may not ensure absolute safety, it may leadto a scenario where very few (if any) accidents occur among autonomousvehicles. For example, where all cars (and other road users) are able tosuccessfully verify that they will not be blamed for an accident as aresult of an action taken, accidents may be eliminated. By definition,for every accident there is at least one responsible car. Thus, if nocar takes an action for which it may be responsible for a resultingaccident (according to the RSS model described above), there shouldnever be any accidents, leading to the type of absolute safety or nearabsolute safety sought by unwieldy and impractical statistical methods.

Not all roads are of a simple structure. Some, like junctions androundabouts, contain more complex situations, along with various rightof way rules. Not all occluded objects are cars or pedestrians, withbicycles and motorcycles all legitimate road users to be considered. Theprinciples introduced in this section may be extended to theseadditional cases.

Efficiently Validated Conditions for Responsibility-Sensitive Safety

This section discusses implementation aspects of RSS. To begin, itshould be noted that an action that is performed now may have abutterfly effect that will lead to a chain of events with an accidentafter 10 minutes of driving, for example. A “brute-force” approach ofchecking all possible future outcomes not only impractical, it is likelyimpossible. To overcome this challenge, the responsibility-sensitivesafety definitions described above are now described together withcomputationally efficient methods to validate them,

Computationally Feasible Safety Verification.

The main mathematical tool for computationally feasible verification is“induction.” To prove a claim by induction, one begins with proving theclaim for simple cases, and then, each induction step extends the proofto more and more involved cases. To illustrate how this induction toolcan be helpful for safety verification, consider again the simpleexample of a car c_(r) following another, c_(f) (FIG. 21). The followingconstraint may be applied on the policy of c_(r). At each time step t,the policy can pick any acceleration command such that even if c_(f)will apply a deceleration of −a_(max), the resulting distance betweenc_(r) and c_(f) at the next time step will be at least the safelongitudinal distance (defined in Definition 3 and Lemma 2). If no suchaction exists, c_(r) must apply the deceleration −a_(max). The followinglemma uses induction to prove that any policy that adheres to the aboveconstraints will never make an accident with c_(f).

Lemma 3 Under the assumptions given in Definition 3, if the policy q,c_(r) adheres to the constraints given above if will never make anaccident with c_(f).

Proof The proof is by induction. For the induction base, start with aninitial state in which the distance between the two cars is safe(according to Lemma 2). The induction step is as follows. Consider thedistance between c_(r) and c_(f) at some time t. If there is an actionthat results in a safe distance (even with c_(f) making maximaldeceleration), we are fine. If all actions cannot guarantee safedistance, let t′<t be the maximal time in which we took an action whichwas not maximal deceleration. By the induction hypothesis, at time t′+1,we were in a safe distance, and from there on we performed maximaldeceleration. Hence, by the definition of safe distance, there was nocrash from time t′ till now, which concludes the proof.

The above example demonstrates a more general idea: there's someemergency maneuver which can be performed by c_(r) in an extreme case,and lead it back to a “safe state.” It should be noted that theconstraints on the policy we have described above depend on just onefuture time step, hence it can be verified in a computationallyefficient manner.

To generalize those ideas of sufficient local properties for RSS, wefirstly define a Default Emergency Policy (DEP), and use it as abuilding block for defining a local property of action-taking which wecall “cautious”. It is then shown that taking only cautious commands issufficient for RSS.

Definition 12 (Default Emergency Policy) The Default Emergency Policy(DEP) is to apply maximum braking power, and maximum heading changetowards 0 heading w.r.t. the lane. The maximum braking power and headingchange are derived from physical parameters of the car (and maybe alsofrom weather and road conditions). Definition 13 (Safe state) A state sis safe f performing DEP starting from it will not lead to an accidentof our blame. As in the simple case of a car following another, wedefine a command to be cautious if it leads to a safe state. Definition14 (Cautious command) Suppose we are currently at state so. A command ais cautious f the crest state, s₁, will be safe with respect to a set Aof possible commands that other vehicles might perform now. The abovedefinition depends on the worst-case commands, in the set A, othervehicles might perform. We will construct the set A based on reasonableupper bounds on maximum braking/acceleration and lateral movements.

The following theorem proves, by induction again, that if we only issuecautious commands then there will be no accidents of our blame. Theorem1 Assume that in time 0, cis in a safe slate, and for every time step, conly issues cautious commands-, where f no cautious command exists atsome time step, c applies DEP. Then, c will never make accidents of itsblame. Proof By induction. The base of the induction follows from thedefinition of a safe state and step from the definition of a cautiouscommand.

One benefit of this approach is that there may be no need to checkinfinite future, as we can quickly return to a safe state, and continuesafely from there. Moreover, given the fact we will plan again at t+1,and hence be able to perform DEP then if necessary, we should only checkthe command we are giving at time t, and not a possible longer plan wemight have in mind—we can change that plan at t+1. Now, incorporating alearning component in a system, when it is verified at run time by thistransparent model, is made possible. Finally, this local verificationimplies full future RSS, which is our desired goal. An implementationobstacle is that the cautiousness definition involves all trajectoriesanother agent can perform until t_(brake), which, even for moderate is ahuge space. To tackle this, we next turn to develop an efficientlycomputable way to verify cautiousness, and hence RSS, in a scalablemanner.

Efficient Cautiousness Verification

A first observation is that a state is not safe if and only if thereexists a specific vehicle, ĉ, which can perform commands from the set Awhich lead to an accident of our blame while we execute the DEP.Therefore, in a scene with a single target car, denoted ĉ, and in thegeneral case, the procedure may be executed sequentially, for each ofthe other vehicles in the scene.

When considering a single target car, an action a is not cautious if andonly if there is a sequence of commands for ĉ, denoted ã₁, . . .ãt_(brake), all in the set A, that results in an accident of c's blame.As already proven, if at time 0, it holds that {tilde over (c)} is inthe frontal corridor of c, there is a simple way to check thecautiousness of a—we just need to verify that even if {tilde over (c)}will apply maximal brake for one time step (and we'll perform a), theresulting longitudinal distance will remain safe. The lemma below givesa sufficient condition for cautiousness in the more involved cases,where lateral maneuvers are to be considered too.

Lemma 4 Assume that at time T=0 {tilde over (c)} is not in the frontalcorridor of c. Then, fat every T∈(0, t_(brake)], there is no non-safecut in of c's blame, then a is cautious.

Proof Suppose that a is not cautious, namely, there exists ã₁, . . . ,ãt_(brake) that leads to an accident of c's blame. Before the accidentthere roust be a cut-in time, T. Assume first that T>0. If this cut-inwas at a safe longitudinal distance, then there cannot be an accident ofour blame due to the fact that DEP is executed by deceleration of−a_(max) and based on the definition of safe longitudinal distance (andwe assume here that the response time ρ is larger than the timeresolution of steps). If the cut-in was non-safe, by the assumption ofthe lemma it was not of c's blame, hence the accident is also not of c'sblame.

Finally, if T<0, by the assumption of the lemma, at the moment ofcutting, {tilde over (c)} was at the back corridor of c. By induction, cperformed only safe cut-ins in the past, and hence either the cut-in wassafe or it was c's blame. In both cases, the current accident is not ofc's blame.

In light of Lemma 4, the problem of checking whether there can be anon-safe cut in of c's blame remains. An efficient algorithm ispresented below for checking the possibility of a non-safe cut-in attime t. To validate the entire trajectory we discretize the timeinterval [0, t_(brake)] and apply the algorithm on all time intervals(with a slightly larger value of p in the definition of safe distance toensure that the discretization doesn't hurt). Let ĉ_(diag) be the lengthof a diagonal of a minimal rectangle bounding {tilde over (c)}. For eachtime t∈[0, t_(brake)], define c_(length)(i) to be the longitudinal“span” of c in time t, and let

${L(t)} = {\frac{{\overset{\sim}{c}}_{diag} + c_{{length}{\lbrack t\rbrack}}}{2}.}$

Define c_(width)[t] in similar fashion and

${W(t)} = {\frac{{\overset{\sim}{c}}_{diag} + c_{{width}{\lbrack t\rbrack}}}{2}.}$

Algorithm 1: Check the possibility of a non-safe cut-in at time t input; y[0], v _(y)[0], x[0], v _(x)[0] are longitudinal/lateralposition/velocity  of c at time 0  y[t], v_(y)[t], x[t], v_(x)[t] arelongitudinal/lateral position/velocity  of c at time t a_(y,min),a_(y,max) are longitudinal acceleration boundaries a_(x,max) is alateral acceleration absolute value boundary L = L(t), W = W(t) checklongitudinal feasibility: let ŷ_(min) = ŷ[0] + {circumflex over(v)}_(y)[0]t + 1/2 a_(y,min)t² let ŷ_(max) = ŷ[0] + {circumflex over(v)}_(y)[0]t + 1/2 a_(y,max)t² if [ŷ_(min,) ŷ_(max)] ∩ [y[t] − L, y[t] +L] ≠ ∅ continue to check lateral feasibility else if y _(min) > y[t] + Land (y_(min), v _(y)[0] + a_(y,min)t) is not longitudinally safe w.r.t(y[t], v_(y)[t]) continue to check lateral feasibility else if y_(max) <y[t] − L and ( y_(max), v _(y)[0] + a_(y,min)t) is not longitudinallysafe w.r.t (y[t], v_(y)[t]) check lateral feasibility: w.l.o.g. assumex[t] = 0 and x[0] ≤ and v_(x) [0] ≥ 0. if a position x [t] is notconsidered (μ₁, μ₂) - Winning by Lateral Position w.r.t. a position x[t]−W w.l.o.g. assume v_(x) [t] = −μ, as in Definition 6. else w.l.o.g.assume v_(x) t = −2μ as in Definition 6. let t_(top) = 0.5(t-v_(x)[0]/a_(x,max)) If t_(top) < 0 let x_(max) = x[0] + 2(v[0]t_(top) + 0.5a_(x,max) t_(top) ²) + v _(x)[0]²/(2a_(x,max)) if x_(max) < −W return“non-feasible” return “feasible”

The following theorem proves the correctness of the above algorithm.

Theorem 2 If Algorithm 1 returns “non feasible” then there cannot be anon-safe cut-in of the ego vehicle's blame at tune t. To prove thetheorem, we rely on the following key lemmas, which prove thecorrectness of the two building blocks of Algorithm 1. Start with thelongitudinal

Lemma 5 Under the notation of Algorithm 1, if the check longitudinalfeasibility procedure is concluded by returning “‘non-feasible”, thenthere cannot be a non-safe cut-in of the ego vehicle's blame at time t.

Proof Ignoring the lateral aspect of a cut-in maneuver, we examine themere possibility that the longitudinal distance between c and {tildeover (c)} will be unsafe. It is clear that the positions ({tilde over(y)}_(min), ŷ_(max)) are bounding the position which can be attained by{tilde over (c)} at time t. By the fact [{tilde over (y)}_(min), {tildeover (y)}_(max)]∩[y[t]−L, y[t]+L]=Ø, we obtain that any longitudinallynon-safe distance which is attainable, is ≥L. Assume {tilde over(y)}_(min)>y[t]+L, and assume by contradiction that a non-safelongitudinal position and velocity, denoted {tilde over (y)}_(bad) [t],{tilde over (v)}_(ybad)[i], are attainable using acceleration commandsbounded by a_(y,min), a_(y,max). By definition of {tilde over(y)}_(min), we have {tilde over (y)}_(bad)[t]>{tilde over (y)}_(min),and hence the distance between the cars is larger, namely y_(bad)[t]−(y[t]+L)>y _(min)−(y[t]+L). Since ({tilde over(y)}_(min),{tilde over (v)}_(y)[0]+a_(y,min) _(t) ) is longitudinallysafe w.r.t. (y[t], v_(y)[t]), by definition of longitudinal non-safety,it follows that the attained velocity {tilde over (v)}_(ybad)[t] must besmaller than v_(y)[0]+a_(y,min) _(t) . However, it is clear that inorder to achieve lesser speed, e must use average acceleration which islesser than a_(y,min) throughout the time window [0, t], thuscontradicting the fact that the longitudinal non-safety was attainedusing commands bounded by a_(a,min), a_(y,max). By considering asymmetrical argument for the case ŷ_(max)<y[t]−L, the proof iscompleted.

Next, the lateral feasibility.

Lemma 6 Under the notation of Algorithm 1, if the check lateralfeasibility procedure is concluded by returning “non-feasible”, thenthere cannot be a non-safe cut-in of the ego vehicle's blame at time t.

Proof First, it is clear that there is no loss of generality by theassumptions [xt]=0, {tilde over (x)}[0]≤0 and the ones regardingv_(v)[t], by a simple change of coordinates and consideration ofrelative velocity. Moreover, by similar arguments it is simple to extendto the case when {tilde over (v)}_(x)[0]≤0.

Note that the positions of the cars involved in the cut-in, which in ourcase, are (x[t], x[t]−W), imply some (μ1,μ2)—Winning by Lateral Positionproperly, affecting the blame. By our assumptions over v_(x)[t], weobtain that the maximal lateral velocity {tilde over (c)} may use attime t, under assumption that c will be blamed, is 0: either in order toμ-“tie” lateral velocity (in the ease c does not (μ1,μ2)—Win by LateralPosition, this can be enough in order to put the blame on it), or toμ-Win lateral velocity (in the case c does (μ1, μ2)—Win by LateralPosition, this is necessary in order to put the blame on it). It is leftto check whether exists a maneuver starting at {tilde over (v)}_(x)[0],ending at {tilde over (v)}_(x)[t]=0, using lateral accelerations boundedby a_(x,max), with final position {tilde over (x)}[t]≥x[t]−W. In words,a cut-in which ends at the desired lateral velocity, 0.

Recall the definition t_(top)=0.5(t−{circumflex over(v)}_(x)[0]/a_(x,max)) from the algorithm. Assume t_(top)<0. Thisimplies that the time needed by {tilde over (c)} in order to reachlateral velocity 0 when using maximal lateral acceleration, namely,{tilde over (v)}_(x)[0]/a_(x,max), is lesser than t. This implies thatthere is no manoeuvre which it can perform in order to reach the desiredvelocity in time, and hence no problematic maneuver exists. Therefore,if the procedure returned “non-feasible” due to t_(top)<0, indeed, thereis no feasibility of a non-safe cut-in of c's blame.

Consider the case t_(top)>0. Then, the procedure returned “non-feasible”due to x_(max)<−W. Consider a family of lateral velocity profiles for{tilde over (c)} in the time range [0,t], denoted U={u_(a): a>{tildeover (v)}_(x)[0]/t} and parameterized by a. We define, for each a, insimilar fashion to the one used in the algorithm,t_(top)(a):=0.5(t−{tilde over (v)}_(x)[0]/a). Note that t_(top)(a)>0 forall a>{tilde over (v)}_(x)[0]/t. We now define the velocity profile u,for all times t′∈[0, t] as follows:

${u_{a}\left( t^{\prime} \right)} = \left\{ \begin{matrix}{{{\overset{\sim}{v}}_{x}\lbrack 0\rbrack} + {a \cdot t^{\prime}}} & {t^{\prime} < {t_{top}(a)}} \\{{{\overset{\sim}{v}}_{x}\lbrack 0\rbrack} + {a \cdot \left( {{2{t_{top}(a)}} - t^{\prime}} \right)}} & {t^{\prime} \geq {t_{top}(a)}}\end{matrix} \right.$

First, it can be seen that u_(a) satisfies the constraintsu_(a)(0)={tilde over (v)}_(x)[0], u_(o)(t)={tilde over (v)}_(x)[t].Second, the distance travelled while using u_(a) can be calculated, asthis amounts to integration of a piecewise linear function. Define thearrived-at position as {tilde over (x)}_(μ) _(o) , and note that x_(max)defined in the algorithm is precisely

x_(u_(a_(x, max ))).

Third, it can be seen that the travelled distance is monotonicallyincreasing with a, and is unbounded. Hence, for any desired finalposition

${x > {\overset{\sim}{x}}_{u_{{o_{x}{\lbrack 0\rbrack}}/t}}},$

there exists a value of a for which x={tilde over (x)}_(μ) _(o) . Inparticular, for x=x[t]−W, such a value exists, and we denote it bya_(ccl).

Observe that since x_(max), defined in the algorithm, is <x[t]−W, wehave that a_(cut)>a_(x,max). This in not sufficient in order to show novalid maneuver can lead to position ≥x[t]−W; this is implied only formembers of the family U. We now prove that even outside of U, allvelocity profiles which attain a final position of x[t]−W must use anacceleration value of at least a_(cut) on the way, making them invalid,and hence completing the proof.

Assume some velocity profile u satisfies the boundary constraintsu(0)=v_(x)[0], u(t)={tilde over (v)}_(x)[t]. Moreover, assume it attainssome final position {tilde over (x)}_(μ)>x[t]−W. We thus obtain:

∫₀ ^(t) u(τ)dτ≥∫ ₀ ^(t) u _(a) _(cut) (τ)dτ.

Assume u≥u_(a) _(cut) for all τ. In particular,u(t_(tor)(a_(cut)))≥u_(o) _(cut) (t_(top)(a_(cut))). From the mean valuetheorem, there exists ζ∈[0, t_(top)(a_(cut))] s.t.

${{u^{\prime}(\zeta)} = {\frac{{u\left( {t_{top}\left( a_{cut} \right)} \right)} - {u(0)}}{t_{top}\left( a_{cut} \right)} = {{\frac{{u\left( {t_{top}\left( a_{cut} \right)} \right)} - {u_{a_{cut}}(0)}}{t_{top}\left( a_{cut} \right)} \geq \frac{{u_{a_{cut}}\left( {t_{top}\left( a_{cut} \right)} \right)} - {u_{a_{cut}}(0)}}{t_{top}\left( a_{cut} \right)}} = {a_{cut} > a_{x,\max}}}}},$

implying infeasibility of u, as it uses acceleration (that is, u′, thederivative of the velocity) which exceeds a_(x,max).

Now, assume u≥u_(a) _(cut) does not hold for all τ. Then, due to thefact ∫₀ ^(t) u(τ)dτ≥∫₀ ^(t)u_(a) _(cut) (τ)dτ, there must be a pointwhere u>u_(a) _(cut) . If such point τ_(large) exists in[0,t_(top)(a_(cut))], then we can easily use the mean value theorem inthe same manner as above, to obtain ζ∈[0,τ_(large)] where too large anacceleration is used. If such point only exists in [t_(top)(a_(cut)),t],similar argument will give us a point ζ∈[τ_(large),t] in which anacceleration value lesser than −a_(x,max) was used, concluding theproof. Equipped with the above lemmas, Theorem 2's proof is immediate.

Safety Verification—Occlusions

In similar fashion to dealing with observed objects, we can define theextension for cautiousness w.r.t. occluded objects, with a similartheorem to Theorem 1, proving that cautiousness implies there are neveraccidents of our blame.

Definition 15 (Cautiousness w.r.t., Occluded Objects) A command given attime t is Cautious w.r.t. Occluded Objects if in the case that theexposure time of the object is t+1, and we command a Default EmergencyPolicy (DEP) at t+1, there will not be an accident of our blame.

Lemma 7 If we only give cautious, w.r.t. occluded objects and nonoccluded objects, commands, there will never be an accident of ourblame.

Proof Assume that an accident of our blame occurred at time t, with theexposure time being t′≤t. By cautiousness assumption, the command givenat t′−1 allowed us to command a DEP at without being blamed for anaccident. As there was an accident of our blame, we apparently did notcommand a DEP at time t′. But from t′ on, we were safe w.r.t. nonoccluded objects, hence the command we gave was safe, and there was noaccident of our blame.

Here too, we provide efficient ways to checking cautiousness withrespect to a worst-case assumption over occluded objects, allowing forfeasible, scalable, RSS.

Driving Policy

A driving policy is a mapping from a sensing state (a description of theworld around us) into a driving command (e.g., the command is lateraland longitudinal accelerations for the coming second, which determineswhere and at what speed should the car be in one second from now). Thedriving command is passed to a controller, which aims at actually movingthe car to the desired position/speed.

In the previous sections a formal safety model and proposed constraintson the commands issued by the driving policy that guarantee safety weredescribed. The constraints on safety are designed for extreme cases.Typically, we do not want to even need these constraints, and would liketo construct a driving policy that leads to a comfortable ride. Thefocus of this section is on how to build an efficient driving policy, inparticular, one that requires computational resources that can scale tomillions of cars. For now, this discussion does not address the issue ofhow to obtain the sensing state and assume an utopic sensing state, thatfaithfully represents the world around us without any limitations. Latersections discuss the effect of inaccuracies in the sensing state on thedriving policy.

The problem of defining a driving policy is cast in the language ofReinforcement Learning (RL), as discussed in the sections above. At eachiteration of Rio, an agent observes a state describing the world,denoted s_(h) and should pick an action, denoted a_(t), based on apolicy function, π, that maps states into actions. As a result of itsaction and other factors out of its control (such as the actions ofother agents), the state of the world is changed to s_(f)+1. We denote a(state, action) sequence by s=((s₁,a₁), (s₂,a₂), . . . ,(s_(len(s)),a_(len(s)))). Every policy induces a probability functionover (state, action) sequences. This probability function may beaffected by the actions taken by the agent, but also depends on theenvironment (and in particular, on how other agents behave). We denoteby P_(x) the probability over (state, action) sequences induced by π.The quality of a policy is defined to be

_(s˜P) _(π) [ρ(s)], where p(s) is a reward function that measures howgood the sequences s is. In most case, ρ(s) takes the form ρ(s)=Σ_(t=1)^(len(s)) ρ(s_(t), a_(t)), where ρ(s, a) is an instantaneous rewardfunction that measures the immediate quality of being at states andperforming action a. For simplicity, we stick to this simpler case.

To cast the driving policy problem in the above RL language, let s_(t)be some representation of the road, and the positions, velocities, andaccelerations, of the ego vehicle as well as other road users. Let a_(t)be a lateral and longitudinal acceleration command. The next state,s_(t+1), depends on a_(t) as well as on how the other agents willbehave. The instantaneous reward, ρ(s_(t), a_(t)), may depend on therelative position/velocities/acceleration to other cars, the differencebetween our speed and the desired speed, whether we follow the desiredroute, whether our acceleration is comfortable etc.

One challenge in deciding what action should the policy take at time tstems from the fact that one needs to estimate the tong term effect ofthis action on the reward. For example, in the context of drivingpolicy, an action that is taken at lime t may seem a good action for thepresent (that is, the reward value ρ(s_(t), a_(t)) is good), but mightlead to an accident after 5 seconds (that is, the reward value in 5seconds would be catastrophic). We therefore need to estimate the longterm quality of performing an action a when the agent is at state s.This is often called the Q-function, namely, Q(s, a) should reflect thelong term quality of performing action a at time s. Given such aQ-function, the natural choice of an action is to pick the one withhighest quality, π(s)=argmax_(o) Q(s, a).

The immediate questions are how to define Q and how to evaluate Qefficiently. Let us first make the (completely non-realistic)simplifying assumption that s_(t)+1 is some deterministic function of(s_(t), a_(t)), namely, s_(t)+1=ƒ(s_(t), a_(t)). One familiar withMarkov Decision Processes (′MDPs), will notice that this assumption iseven stronger than the Markovian assumption of MDPs (i.e., that s_(t)+1is conditionally independent of the past given (s_(t), a_(t))). As notedin [5], even the Markovian assumption is not adequate for multi-agentscenarios, such as driving, and we will therefore later relax theassumption.

Under this simplifying assumption, given st, for every sequence ofdecisions for T steps, (a₁, . . . a_(t)+_(T)), we can calculate exactlythe future states (s_(t)+1, . . . , s_(t)+_(t)+1) as well as the rewardvalues for times t, . . . , T. Summarizing all these reward values intoa single number, e.g. by taking their sum Σ_(τ=t) ^(T) ρ(s_(t), a_(t)),we can define Q(s, a) as follows:

${{Q\left( {s,a} \right)} = {{\max\limits_{({{a_{t,\ldots \;,}a_{t}} + T})}{\sum_{\tau = t}^{T}{{\rho \left( {s_{\tau},a_{\tau}} \right)}\mspace{14mu} {s.t.s_{t}}}}} = s}},{a_{t} = a},{\forall\tau},{s_{\tau + 1} = {f\left( {s_{\tau},a_{\tau}} \right)}}$

That is, Q(s, a) is the best future we can hope for, if we are currentlyat states and immediately perform action a.

Let us discuss how Q may be calculated. The first idea is to discretizethe set of possible actions, A, into a finite set Â, and simply traverseall action sequences in the discretized set. Then, the runtime isdominated by the number of discrete action sequences, |Â|^(T). If Ârepresents 10 lateral accelerations and 10 longitudinal accelerations,we obtain 100^(T) possibilities, which becomes infeasible even for smallvalues of T. While there are heuristics for speeding up the search (e.g.coarse-to-fine search), this brute-force approach requires tremendouscomputational power.

The parameter T is often called the “time horizon of planning”, and itcontrols a natural tradeoff between computation time and quality ofevaluation—the larger T is, the better our evaluation of the currentaction (since we explicitly examine its effect deeper into the future),but on the other hand, a larger T increases the computation timeexponentially. To understand why we may need a large value of T,consider a scenario in which we are 200 meters before a highway exit andwe should take it. When the time horizon is long enough, the cumulativereward will indicate if at some timer between t and t+T we have arrivedto the exit lane. On the other hand, for a short time horizon, even ifwe perform the right immediate action we will not know if it will leadus eventually to the exit lane.

A different approach attempts to perform offline calculations in orderto construct an approximation of Q, denoted {circumflex over (Q)}, andthen during the online run of the policy, use {circumflex over (Q)} asan approximation to Q, without explicitly rolling out the future. Oneway to construct such an approximation is to discretize both the actiondomain and the state domain. Denote by Â, Ŝ these discretized sets. Anoffline calculation may evaluate the value of Q(s, a) for every (s,a)∈Ŝ×Â. Then, for every a∈Â we define {circumflex over (Q)}(s_(t), a) tobe Q(s, a) for s=argmin_(aŜ)∥s−s_(t)∥. Furthermore, based on thepioneering work of Gellman [2, 3], we can calculate Q(s, a) for every(s, a)∈Ŝ×Â, based on dynamic programming procedures (such as the ValueIteration algorithm), and under our assumptions, the total runtime isorder of T|Â| |Ŝ|. The main problem with this approach is that in anyreasonable approximation, Ŝ is extremely large (due to the curse ofdimensionality). Indeed, the sensing slate should represent 6 parametersfor every other relevant vehicle in the sense—the longitudinal andlateral position, velocity, and acceleration. Even if we diseretize eachdimension to only 10 values (a very crude discretization), since we have6 dimensions, to describe a single car we need 10⁶ states, and todescribe k cars we need 10^(6k) states. This leads to unrealistic memoryrequirements for storing the values of Q for every (s, a) in Ŝ×Â.

One approach for dealing with this curse of dimensionality is torestrict Q to come from a restricted class of functions (often called ahypothesis class), such as linear functions over manually determinedfeatures or deep neural networks. For example, consider a deep neuralnetwork that approximates Q in the context of playing Atari games. Thisleads to a resource-efficient solution, provided that the class offunctions that approximate Q can be evaluated efficiently. However,there are several disadvantages of this approach. First, it is not knownif the chosen class of functions contains a good approximation to thedesired Q function. Second, even if such function exists, it is notknown if existing algorithms will manage to learn it efficiently. Sofar, there are not many success stories for learning a Q function forcomplicated multi-agent problems, such as the ones we are facing indriving. There are several theoretical reasons why this task isdifficult. As mentioned regarding the Markovian assumption, underlyingexisting methods are problematic. But, a more severe problem is a verysmall signal-to-noise ratio due to the time resolution of decisionmaking, as explained below.

Consider a simple scenario in which a vehicle needs to change lane inorder to take a highway exit in 200 meters and the road is currentlyempty. The best decision is to start making the lane change. Decisionsmay be made every 0.1 second, so at the current time t, the best valueof Q(s_(t), a) should be for the action a corresponding to a smalllateral acceleration to the right. Consider the action a′ thatcorresponds to zero lateral acceleration. Since there is a very littledifference between starting the change lane now, or in 0.1 seconds, thevalues of Q(s_(t), a) and Q(s_(t), a′) are almost the same. In otherwords, there is very little advantage for picking a over a′. On theother hand, since we are using a function approximation for Q, and sincethere is noise in measuring the state it is likely that ourapproximation to the Q value is noisy. This yields a very smallsignal-to-noise ratio, which leads to an extremely slow learning,especially for stochastic learning algorithms which are heavily used forthe neural networks approximation class. However, as noted in, thisproblem is not a property of any particular function approximationclass, but rather, it is inherent in the definition of the Q function.

In summary, available approaches can be roughly divided into two camps.The first one is the brute-force approach which includes searching overmany sequences of actions or discretizing the sensing state domain andmaintaining a huge table in memory. This approach can lead to a veryaccurate approximation of Q but requires unlimited resources, either interms of computation time or in terms of memory. The second one is aresource efficient approach in which we either search for shortsequences of actions or we apply a function approximation to Q. In bothcases, we pay by having a less accurate approximation of Q that mightlead to poor decisions.

The approach described herein includes constructing a Q function that isboth resource-efficient and accurate is to depart from geometricalactions and to adapt a semantic action space, as described in the nextsubsection.

Semantic Approach

As a basis for the disclosed semantic approach, consider a teenager thatjust got his driving license. His father sits next to him and gives him“driving policy” instructions. These instructions are not geometric—theydo not take the form “drive 13.7 meters at the current speed and thenaccelerate at a rate of 0.8 m/s²”. Instead, the instructions are ofsemantic nature—“follow the car in front of you” or “quickly overtakethat car on your left” We formalize a semantic language for suchinstructions, and use them as a semantic action space. We then definethe Q function over the semantic action space. We show that a semanticaction can have a very long time horizon, which allows us to estimateQ(s, a) without planning for many future semantic actions. Yes, thetotal number of semantic actions is still small. This allows us toobtain an accurate estimation of the Q function while still beingresource efficient. Furthermore, as we show later, we combine learningtechniques for further improving the quality function, while notsuffering from a small signal-to-noise ratio due to a significantdifference between different semantic actions.

Now define a semantic action space. The main idea is to define lateraland longitudinal goals, as well as the aggressiveness level of achievingthem. Lateral goals are desired positions in lane coordinate system(e.g., “my goat is to be in the center of lane number 2”). Longitudinalgoals are of three types. The first is relative position and speed withrespect to other vehicles (e.g., “my goal is to be behind car number 3,at its same speed, and at a distance of 2 seconds from it”). The secondis a speed target (e.g., “drive at the allowed speed for this road times110%”). The third is a speed constraint at a certain position (e.g.,when approaching a junction, “speed of 0 at the stop line”, or whenpassing a sharp curve, “speed of at most 60 km/h at a certain positionon the curve”). For the third option, we can instead apply a “speedprofile” (few discrete points on the route and the desired speed at eachof them). A reasonable number of lateral goals is bounded by 16=4×4 (4positions in at most 4 relevant lanes). A reasonable number oflongitudinal goals of the first type is bounded by 8×2×3=48 (8 relevantcars, whether to be in front or behind them, and 3 relevant distances).A reasonable number of absolute speed targets are 10, and a reasonableupper bound on the number of speed constraints is 2. To implement agiven lateral or longitudinal goal, we need to apply acceleration andthen deceleration (or the other way around). The aggressiveness ofachieving the goal is a maximal (in absolute value)acceleration/deceleration to achieve the goal. With the goal andaggressiveness defined, we have a closed form formula to implement thegoal, using kinematic calculations. The only remaining part is todetermine the combination between the lateral and longitudinal goals(e.g., “start with the lateral goal, and exactly at the middle of it,start to apply also the longitudinal goal”). A set of 5 mixing times and3 aggressiveness levels seems more than enough. All in all, we haveobtained a semantic action space whose size is ≈10⁴.

It is worth mentioning that the variable time required for fulfillingthese semantic actions is not the same as the frequency of thedecision-making process. To be reactive to the dynamic world, we shouldmake decisions at a high frequency—in our implementation, every 100 ms.In contrast, each such decision is based on constructing a trajectorythat fulfills some semantic action, which will have a much longer timehorizon (say, 10 seconds). We use the longer time horizon since it helpsus to better evaluate the short-term prefix of the trajectory. The nextsubsection discusses the evaluation of semantic actions, but beforethat, we argue that semantic actions induce a sufficient search space.

As discussed above, a semantic action space induces a subset of allpossible geometrical curves, whose size is exponentially smaller (in T)than enumerating all possible geometrical curves. The first immediatequestion is whether the set of short-term prefixes of this smallersearch space contains all geometric commands that we will ever want touse. This is indeed sufficient in the following sense, if the road isfree of other agents, then there is no reason to make changes exceptsetting a lateral goal and/or absolute acceleration commands and/orspeed constraints on certain positions. If the road contains otheragents, we may want to negotiate the right of way with the other agents.In this case, it suffices to set longitudinal goals relatively to theother agents. The exact implementation of these goals in the long runmay vary, but the short-term prefixes will not change by much. Hence, weobtain a very good cover of the relevant short-term geometricalcommands.

Constructing an Evaluation Function for Semantic Actions

We have defined a semantic set of actions, denoted by A^(s). Given thatwe are currently in state, s, we need a way to choose the besta^(v)∈A^(s). To tackle this problem, we follow a similar approach to theoptions mechanism of [6]. The basic idea is to think of a^(s) as ameta-action (or an option). For each choice of a meta-action, weconstruct a geometrical trajectory (s₁, a₁), . . . (s_(r), a_(r)) thatrepresents an implementation of the meta-action, a^(s). To do so we ofcourse need to know how other agents will react to our actions, but fornow we are still relying on (the non-realistic) assumption thats_(t+1)=ƒ(s_(t), a_(t)) for some known deterministic function ƒ. We cannow use

$\frac{1}{T}{\sum_{\tau = t}^{T}{\rho \left( {s_{\tau},a_{\tau}} \right)}}$

as a good approximation of the quality of performing the semantic actiona^(s) when we are at state s¹.

This approach can yield a powerful driving policy. However, in somesituations a more sophisticated quality function may be needed. Forexample, suppose that we are following a slow truck before an exit lane,where we need to take the exit lane. One semantic option is to keepdriving slowly behind the truck. Another one is to overtake the truck,hoping that later we can get back to the exit lane and make the exit ontime. The quality measure described previously does not consider whatwill happen after we will overtake the truck, and hence we will notchoose the second semantic action even if there is enough time to makethe overtake and return to the exit lane. Machine learning can help usto construct a better evaluation of semantic actions that will take intoaccount more than the immediate semantic actions. As previouslydiscussed, learning a Q function over immediate geometric actions isproblematic due to the low signal-to-noise ratio (the lack ofadvantage). This is not problematic when considering semantic actions,both because there is a large difference between performing thedifferent semantic actions and because the semantic time horizon (howmany semantic actions we take into account) is very small (probably lessthan three in most cases).

Another potential advantage of applying machine learning is for the sakeof generalization: we may set an adequate evaluation function for everyroad, by a manual inspection of the properties of the road, which mayinvolve some trial and error. Here, a machine learning approach, asdiscussed above, can be trained on a large variety of road types so asto generalize to unseen roads as well. The semantic action spaceaccording to the disclosed embodiments may allow for potential benefits:semantic actions contain information on a long-time horizon, hence wecan obtain a very accurate evaluation of their quality while beingresource efficient.

The Dynamics of the Other Agents

So far, we have relied on the assumption that s_(t+1) is a deterministicfunction of s_(t) and a_(t).

As emphasized previously, this assumption is not completely realistic asour actions affect the behavior of other road users. While we do takeinto account some reactions of other agents to our actions (for example,we assume that if we will perform a safe cut-in than the car behind uswill adjust its speed so as not to hit us from behind), it is notrealistic to assume that we model all of the dynamics of other agents.The solution to this problem is to re-apply the decision making at ahigh frequency, and by doing this, constantly adapt our policy to theparts of the environment that are beyond our modeling. In a sense, onecan think of this as a Markovization of the world at every step.

Sensing

This section describes the sensing state, which is a description of therelevant information of the scene, and forms the input to the drivingpolicy module. By and large, the sensing state contains static anddynamic objects. The static objects are lanes, physical road delimiters,constraints on speed, constraints on the right of way, and informationon occluders (e.g., a fence that occludes relevant part of a mergingroad). Dynamic objects are vehicles (e.g., hounding box, speed,acceleration), pedestrians (bounding box, speed, acceleration), trafficlights, dynamic road delimiters (e.g., cones at a construction area),temporary traffic signs and police activity, and other obstacles on theroad (e.g., an animal, a mattress that fell from a truck, etc.).

In any reasonable sensor setting, we cannot expect to obtain the exactsensing state, s. Instead, we view raw sensor and mapping data, which wedenote by x∈X, and there is a sensing system that takes x and producesan approximate sensing state.

Definition 16 (Sensing system) Let S denotes the domain of sensing stateand let X be the domain of raw sensor and mapping data. A sensing systemis a function ŝ: X→S.

It is important to understand when we should accept s(x) as a reasonableapproximation to s. The ultimate way to answer this question is byexamining the implications of this approximation on the performance ofour driving policy in general, and on the safety in particular.Following our safety-comfort distinction, here again we distinguishbetween sensing mistakes that lead to non-safe behavior and sensingmistakes that affect the comfort aspects of the ride. Before addressingthe details, the type of errors a sensing system might make include:

-   -   False negative: the sensing system misses an object.    -   False positive: the sensing system indicates a “ghost” object    -   Inaccurate measurements: the sensing system correctly detects an        object but incorrectly estimates its position or speed    -   Inaccurate semantic: the sensing system correctly detects an        object but misinterpret its semantic meaning, for example, the        color of a traffic light

Comfort

Recall that for a semantic action a, we have used (As, a) to denote ourevaluation of a given that the current sensing state is s. Our policypicks the action π(s) argmax_(a) Q(s, a). If we inject ŝ(x) instead of sthen the selected semantic action would be π(ŝ(x))=argmax_(a) Q(s(x),a). If π(ŝ(x))=π(s) then ŝ(x) should be accepted as a good approximationto s. But, it is also not bad at all to pick π(ŝ(x)) as long as thequality of π (ŝ(x)) w.r.t. the true state, s, is almost optimal, namely,Q(s, π(ŝ(x)))≥Q(s, π(s)))−ϵ, for some parameter ϵ. We say that ŝ isϵ-accurate w.r.t. in such case. Naturally, we cannot expect the sensingsystem to be ϵ-accurate all the time. We therefore also allow thesensing system to fail with some small probability δ. In such a case wesay that ŝ is Probably (w.p. of at least 1−δ), Approximately (up to ϵ),Correct, or PAC for short (borrowing Valiant's PAC teaming terminology).

We may use several (ϵ, δ) pairs for evaluating different aspects of thesystem. For example, we can choose three thresholds, ϵ₁<ϵ₂<ϵ₃ torepresent mild, medium, and gross mistakes, and for each one of them seta different value of δ. This leads to the following definition.

Definition 17 (PAC sensing system) Let ((ϵ₁, δ₁), . . . , (δ_(k),δ_(k))) be a set of (accuracy, confidence) pairs, let S be the sensingstale domain, let X be the raw sensor and mapping data domain, and let Dbe a distribution over X×S. Let A be an action space, Q: S×A→

be a quality function, and π: S→A be such that π(s)∈argmax_(o) Q(s, a).A sensing system, ŝ: X→S, is Probably-Approximately-Correct (PAC) withrespect to the above parameters for every i∈{1, . . . , k} we have thatP_((x,y)˜D)[Q(s, π(ŝ(x)))≥Q(s, π(s))−ϵ_(i)]≥1−δ_(i).

Here, the definition depends an a distribution D over X×S. It isimportant to emphasize that we construct this distribution by recordingdata of: any human drivers but not by following the particular policy ofour autonomous vehicle. While the latter seems more adequate, itnecessitates online validation, which makes the development of thesensing system impractical. Since the effect of any reasonable policy onD is minor, by applying simple data augmentation techniques we canconstruct an adequate distribution and then perform offline validationafter every major update of the sensing system. The definition providesa sufficient, but not necessary, condition for comfort ride using ŝ. Itis not necessary because it ignores the important fact that short termwrong decisions have little effect on the comfort of the ride. Forexample, suppose that there is a vehicle 100 meters ahead, and it isslower than the host vehicle. The best decision would be to startaccelerating slightly now. If the sensing system misses this vehicle butwill detect it in the next time (after 100 milli-seconds), then thedifference between the two rides will not be noticeable. To simplify thepresentation, we have neglected this issue and required a strongercondition. The adaptation to a multi-frame PAC definition isconceptually straightforward but is more technical.

We next derive design principles that follow from the above PACdefinition. Recall that we have described several types of sensingmistakes. For mistakes of types false negative, false positive, andinaccurate semantic, either the mistakes will be on non-relevant objects(e.g., a traffic light for left turn when we are proceeding straight),or they will be captured by the δ part of the definition. We thereforefocus on the “inaccurate measurements” type of errors, which happensfrequently.

Somewhat surprisingly, we will show that the popular approach ofmeasuring the accuracy of a sensing system via ego-accuracy (that is, bymeasuring the accuracy of position of every object with respect to thehost vehicle) is not sufficient for ensuring PAC sensing system. We willthen propose a different approach that ensures PAC sensing system andwill show how to obtain it efficiently.

We start with some additional definitions.

For every object o in the scene, let p(o), {circumflex over (p)}(o) bethe positions of o in the coordinate system of the host vehicleaccording to s, {tilde over (s)}(x), respectively. Note that thedistance between o and the host vehicle is ∥p∥. The additive error of{circumflex over (p)} is ∥p(o)−{tilde over (p)}(o)∥. The relative errorof {circumflex over (p)}(o), w.r.t. the distance between o and the hostvehicle, is the additive error divided by ∥p(o)∥, namely

$\frac{\left. ||{{\hat{p}(o)} - {p(o)}} \right.||}{\left. ||{p(o)} \right.||}.$

It is not realistic to require that the additive error is small for faraway objects. Indeed, consider o to be a vehicle at a distance of 150meters from the host vehicle, and let ϵ be of moderate size, say ϵ=0.1.For additive accuracy, it means that we should know the position of thevehicle up to 10 cm of accuracy. This is not realistic for reasonablypriced sensors. On the other hand, for relative accuracy we need toestimate the position up to 10%, which amounts to 15 m of accuracy. Thisis feasible to achieve (as described below).

A sensing system, ŝ, positions a set of objects, O, in an ϵ-ego-accurateway, if for every o∈O, the (relative) error between p(o) and {circumflexover (p)}(o) is at most ϵ. The following example demonstrates that anϵ-ego-accurate sensing state does not guarantee PAC sensing system withrespect to every reasonable Q. Indeed, consider a scenario in which thehost vehicle drives at a speed of 30 m/s, and there is a stopped vehicle150 meters in front of it. If this vehicle is in the ego lane, and thereis no option to change lanes in time, we must start decelerating now ata rate of at least 3 m/s² (otherwise, we will either not stop in time orwe will need to decelerate strongly later). On the other hand, if thevehicle is on the side of the road, we don't need to apply a strongdeceleration. Suppose that p(o) is one of these cases while {circumflexover (p)}(o) is the other case, and there is a 5 meters differencebetween these two positions. Then, the relative error of {circumflexover (p)}(o) is

$\frac{\left. ||{{\hat{p}(o)} - {p(o)}} \right.||}{\left. ||{p(o)} \right.||} = {\frac{5}{150} = {\frac{1}{30} \leq {0.03{4.}}}}$

That is, the sensing system may be ϵ-ego-accurate for a rather smallvalue of ϵ (less than 3.5% error), and yet, for any reasonable Qfunction, the values of Q are completely different since we areconfusing between a situation in which we need to brake strongly and asituation in which we do not need to brake strongly.

The above example shows that ϵ-ego-accuracy tides not guarantee that oursensing system is PAC. Whether there is another property that issufficient for PAC sensing system depends on Q. We will describe afamily of Q functions for which there is a simple property of thepositioning that guarantees PAC sensing system. The problem ofϵ-ego-accuracy is that it might lead to semantic mistakes—in theaforementioned example, even though ŝ was ϵ-ego-accurate with ϵ<3.5%, itmis-assigned the vehicle to the correct lane. To solve this problem, werely on semantic units for lateral position.

Definition 18 (semantic units) A lane center is a simple natural curve,namely, it is a differentiable, infective, mapping

: [a, b]→

³, where for every a≤t₁<t₂≤b we have that the length Length (t₁,t₂):=∫_(r=t) ₁ ^(t) ² |

′^((τ)|dτ equals to)

₂−

₁. The width of the lane is a function w: [a, b]→

_(t). The projection of a point x∈

₃ onto the curve is the point on the curve closest to x, namely, thepoint

(

_(x)) for t_(x)=argmin_(i∈|a,b|)∥

(l)−x∥. The semantic longitudinal position of x w.r.t. the lane is t_(x)and the semantic lateral position of x w.r.t. the lane is

(

_(x))/w(

_(x)). Semantic speed and acceleration are defined as first and secondderivatives of the above.

Similarly to geometrical units, for semantic longitudinal distance weuse relative error: if ŝ induces a se antic longitudinal distance of{circumflex over (p)}(o) for some object, while the true distance isp(o), then the relative error is

$\frac{\left| {{\hat{p}(o)} - {p(o)}} \right|}{\max \left\{ {{p(o)},1} \right\}}$

(where the maximum in the denominator deals with cases in which theobject has almost the same longitudinal distance (e.g., a car next to uson another lane). Since semantic lateral distances are small we can useadditive error for them. This leads to the following definition:

Definition 19 (error in semantic units) Let

be a lane and suppose that the semantic longitudinal distance of thehost vehicle w.r.t. the lane is 0. Let x∈

³ be a point and let {circumflex over (p)}_(lat)(x), {circumflex over(p)}_(lon)(x) be be the semantic lateral and longitudinal distances tothe point w.r.t. the lane. Let {circumflex over (p)}_(lat)(x),{circumflex over (p)}_(lon)(x) be approximated measurements. Thedistance between {circumflex over (p)} and p w.r.t. x is defined as

${d\left( {\hat{p},{p;x}} \right)} = {\max \left\{ {\left| {{{\hat{p}}_{lat}(x)} - {p_{lat}(x)}} \right|,\frac{\left| {{{\hat{p}}_{lon}(x)} - {p_{lon}(x)}} \right|}{\max \left\{ {{p_{lon}(x)},1} \right\}}} \right\}}$

The distance of the lateral and longitudinal velocities is definedanalogously. Equipped with the above definition, we are ready to definethe property of Q and the corresponding sufficient condition for PACsensing system.

Definition 20 (Semantically-Lipschitz Q) A Q function isL-semantically-Lipschitz if for every a, s, ŝ, |Q(s, a)−Q(ŝ(x), a)|≤Lmax, d({circumflex over (p)}, p; o), where {circumflex over (p)}, p arethe measurements induced by s, ŝ on an object o.

As an immediate corollary we obtain:

Lemma 8 If is L-semantically-Lipschitz and a sensing system ŝ producessemantic measurements such that with probability of at least 1δ we haved({circumflex over (p)}, p; o)≤∈/L, then ŝ is a PAC sensing system withparameters ∈, δ.

Safety

This section discusses the potential for sensing errors that can lead tounwanted behaviors. As mentioned before, the policy is provably safe, inthe sense that it won't lead to accidents of the host AV's blame. Suchaccidents might still occur due to hardware failure (e.g., a breakdownof all the sensors or exploding tire on the highway), software failure(a significant bug in some of the modules), or a sensing mistake. Ourultimate goal is that the probability of such events will be extremelysmall—a probability of 10⁻⁹ for such an accident per hour. To appreciatethis number, the average number of hours driver in the U.S. spends onthe road is (as of 2016) less than 300 hours. So, in expectation, onewould need to live 3.3 million years to be in an accident resulting fromone of these types of events.

We first define what is a safety-related sensing error. Recall that atevery step, our policy picks the value of a that maximizes Q(s, a),namely, π(s)=argmax_(a) Q(s, a). We ensure safety by letting Q(s, a)=−∞for every action a that is not cautious (see Definition 14). Therefore,the first type of safety-critic sensing mistake is if our sensing systemleads to picking a non-safe action. Formally, letting π(ŝ(x))=argmax_(a)Q(ŝ(x), a) be the decision according to ŝ, we say that ŝ leads to asafety-critic miss if Q(s, π(ŝ(x)))=−∞. The second type of safety-criticsensing mistake is if all the actions are non-safe according to ŝ(x),and we must apply the standard emergency policy (e.g., braking hard),while according to s there is a safe action, namely, max_(a) Q(s, a)>−∞.This is dangerous when our speed is high and there is a car behind us.We call such mistake a safety-critic ghost.

Usually, a safety-critic miss is caused by a false negative while asafety-critic ghost is caused by a false positive. Such mistakes canalso be caused from significantly incorrect measurements, but in mostcases, our comfort objective ensures we are far away from the boundaryof the safety definitions, and therefore reasonable measurements errorsare unlikely to lead to a safety-critic mistake. How can we ensure thatthe probability of safety-critic mistakes will be very small, say,smaller than 10⁻⁹ per hour? As followed from Lemma 1, without makingfurther assumptions we need to check our system on more than 10⁹ hoursof driving. This is unrealistic (or at least extremely challenging)—itamounts to recording the driving of 3.3 million cars over a year.Furthermore, building a system that achieves such a high accuracy is agreat challenge. A solution for both the system design and validationchallenges is to rely on several sub-systems, each of which isengineered independently and depends on a different technology, and thesystems are fused together in a way that ensures boosting of theirindividual accuracy.

Suppose we build three sub-systems, denoted, s₁, s₂, s₃ (the extensionto more than 3 is straightforward). Each sub-system receives a andshould output safe/non-safe. Actions for which the majority of thesub-systems (2 in our case) accept as safe are considered safe. If thereis no action that is considered safe by at least 2 sub-systems, then thedefault emergency policy is applied. The performance of this fusionscheme is analyzed as follows based on the following definition:

Definition 21 (One side c-approximate independent) Two Bernoulli randomvariables r₁, r₂ are called one side c-approximate independent if

[r ₁ ∧r ₂]≤c

[r ₁]

[r ₂].

For i∈{1,2,3}, denote by e_(i) ^(m), e_(i) ^(g) the Bernoulli randomvariables that indicate if sub-system i performs a safety-criticmiss/ghost respectively. Similarly, e^(m), e^(g) indicate asafety-critic miss/ghost of the fusion system. We rely on the assumptionthat for any pair i≠j, the random variables e_(i) ^(m), e_(j) ^(m) areone sided c-approximate independent, and the same holds for e_(i) ^(g),e_(j) ^(g). Before explaining why this assumption is reasonable, let usfirst analyze its implication. We can bound the probability of e^(m) by:

${{\mathbb{P}}\left\lbrack e^{m} \right\rbrack} = {{{{{\mathbb{P}}\left\lbrack {e_{1}^{m}e_{2}^{m}e_{3}^{m}} \right\rbrack} + {\sum\limits_{j = 1}^{3}\; {{\mathbb{P}}\left\lbrack {{e_{j}^{m}}_{i \neq j}e_{i}^{m}} \right\rbrack}}} \leq {{3{{\mathbb{P}}\left\lbrack {e_{1}^{m}e_{2}^{m}e_{3}^{m}} \right\rbrack}} + {\sum\limits_{j = 1}^{3}\; {{\mathbb{P}}\left\lbrack {{e_{j}^{m}}_{i \neq j}e_{i}^{m}} \right\rbrack}}}} = {{\sum\limits_{j = 1}^{3}\; {{\mathbb{P}}\left\lbrack {_{i \neq j}e_{i}^{m}} \right\rbrack}} \leq {c{\sum\limits_{j = 1}^{3}\; {\prod\limits_{i \neq j}\; {{{\mathbb{P}}\left\lbrack e_{i}^{m} \right\rbrack}.}}}}}}$

Therefore, if all sub-systems have

[e_(i) ^(m)]<p then

[e^(m)]≤3cp². The exact same derivation holds for the safety-criticghost mistakes. By applying a union bound we therefore conclude:

Corollary 2 Assume that for any pair i≠j, the random variables e_(i)^(n), e_(j) ^(m) are one sided c-approximate independent, and the sameholds for e_(i) ^(g), e_(j) ^(g). Assume also that for every i,

[e_(i) ^(m)]≤p and

[e_(i) ^(g)]≤p. Then,

[e _(m) ∨e ^(g)]≤6cp ₂.

This corollary allows us to use significantly smaller data sets in orderto validate the sensing system. For example, if we would like to achievea safety-critic mistake probability of 10⁻⁹, instead of taking order of10⁹ examples, it suffices to take order of 10⁵ examples and test eachsystem separately.

There may be pairs of sensors that yield non-correlated errors. Forexample, radar works well in bad weather conditions but might fail dueto non-relevant metallic objects, as opposed to camera that is affectedby bad weather but is not likely to be affected by metallic objects.Seemingly, camera and lidar have common sources of error—e.g., both areaffected by foggy weather, heavy rain, or snow. However, the type oferrors for camera and lidar would be different—a camera might missobjects due to bad weather and lidar might detect a ghost due toreflections from particles in the air. Since we have distinguishedbetween the two types of errors, the approximate independency is stilllikely to hold.

Our definition of safety-important ghost requires that all actions arenon-safe by at least two sensors. Even in difficult conditions heavyfog), this is unlikely to happen. The reason is that in such situations,systems that are affected by the difficult conditions (e.g., the lidar),will dictate a very defensive driving, as they can declare high velocityand lateral maneuver to be non-safe actions. As a result, the host AVwill drive slowly, and then even if an emergency stop is required, it isnot dangerous due to the low speed of driving. Therefore, our definitionyields an adaptation of the driving style to the conditions of the road.

Building a Scalable Sensing System

The requirements from a sensing system, both in terms of comfort andsafety, have been described. Next, an approach for building a sensingsystem that meets these requirements while being scalable is described.There are three main components of the sensing system. The first is longrange, 360 degrees coverage, of the scene based on cameras. The threemain advantages of cameras are: (1) high resolution, (2) texture, (3)price. The low price enables a scalable system. The texture enables tounderstand the semantics of the scene, including lane marks, trafficlight, intentions of pedestrians, and more. The high resolution enablesa long range of detection. Furthermore, detecting lane marks and objectsin the same domain enables excellent semantic lateral accuracy. The twomain disadvantages of cameras are: (1) the information is 2D andestimating longitudinal distance is difficult, (2) sensitivity tolighting conditions (low sun, bad weather). We overcome thesedifficulties using the next two components of our system.

The second component of our system is a semantic high-definition mappingtechnology, called Road Experience Management (REM) (which involvesnavigation based on target trajectories predetermined and stored forroad segments along with an ability to determine precise locations alongthe target trajectories based on the location (e.g., in images) ofrecognized landmarks identified in the environment of the host vehicle).A common geometrical approach to map creation is to record a cloud of 3Dpoints (obtained by a lidar) in the map creation process, and then,localization on the map is obtained by matching the existing lidarpoints to the ones in the map. There are several disadvantages of thisapproach. First, it requires a large memory per kilometer of mappingdata, as we need to save many points. This necessitates an expensivecommunication infrastructure. Second, not all cars may be equipped withlidar sensors, and therefore, the map is updated very infrequently. Thisis problematic as changes in the road can occur (construction zones,hazards), and the “time-to-reflect-reality”of lidar-based mappingsolutions is large. In contrast, REM follows a semantic-based approach.The idea is to leverage the large number of vehicles that are equippedwith cameras and with software that detects semantically meaningfulobjects in the scene (lane marks, curbs, poles, traffic lights, etc.).Nowadays, many new cars are equipped with ADAS systems which can beleveraged for crowd-sourced map creation. Since the processing is doneon the vehicle side, only a small amount of semantic data should becommunicated to the cloud. This allows a very frequent update of the mapin a scalable way. In addition, the autonomous vehicles can receive thesmall sized mapping data over existing communication platforms (thecellular network). Finally, highly accurate localization on the map canbe obtained based on cameras, without the need for expensive lidars.

REM may be used for several purposes. First, it gives us a foresight onthe static structure of the road (we can plan for a highway exit way inadvance). Second, it gives us another source of accurate information ofall of the static information, which together with the camera detectionsyields a robust view of the static part of the world. Third, it solvesthe problem of lifting the 2D information from the image plane into the3D world as follows. The map describes all of the lanes as curves in the3D world. Localization of the ego vehicle on the map enables totrivially lift every object on the road from the image plane to its 3Dposition. This yields a positioning system that adheres to the accuracyin semantic units. A third component of the system may be complementaryradar and lidar systems. These systems may serve two purposes. First,they can offer extremely high levels of accuracy for augmenting safety.Second, they can give direct measurements on speed and distances, whichfurther improves the comfort of the ride.

The following sections include technical lemmas and several practicalconsiderations of the RSS system.

Lemma 9 For all x∈[0,0.1], it holds that 1−x>e^(−2x).

Proof Let ƒ(x)=1−x−e^(−2x). Our goal is to show it is ≥0 for x∈[0,0.1].Note that ƒ(0)=0, and it is therefore sufficient to have that ƒ(x)≥0 inthe aforementioned range. Explicitly, ƒ(x)=−1+2e^(−2x). Clearly,ƒ′(0)=1, and it is monotonically decreasing, hence it is sufficient toverify that ƒ′(0.1) >0, which is easy to do numerically, ƒ′(0.1)≈0.637.

Efficient Cautiousness Verification—Occluded Objects

As with non-occluded objects, we can check whether giving the currentcommand, and after it, the DEP, is RSS. For this, we unroll our futureuntil t_(brake), when assuming the exposure time is 1 and we thencommand DEP, which suffices for cautiousness by definition. For allt′∈[0, t_(brake)], we check whether a blameful accident can occur—whenassuming worst case over the occluded object. We use some of our worstcase maneuvers and safe distance rules. We take an occluder basedapproach to find interest points—namely, for each occluding object, wecalculate the worst case. This is a crucial efficiency-driven approach—apedestrian, for example, can be hidden in many positions behind a car,and can perform many maneuvers, but there's a single worst case positionand maneuver it can perform.

Next, consider the more elaborate case, that of the occluded pedestrian.Consider an occluded area behind a parked car. The closest points in anoccluded area and the front/side of our car c may be found, for example,by their geometrical properties (triangles, rectangles). Formally, wecan consider the occluded area as a union of a small number of convexregions of simple shape, and treat each of them separately. Furthermore,can be seen that a pedestrian can run into the front of the car (underthe v_(limit) constraint) from the occluded area IFF be can do it usingthe shortest path possible. Using the fact that the maximal distancewhich can be travelled by the pedestrian is v_(limit)·t′, we obtain asimple check for a frontal hit possibility. As for a side hit, we notethat in case the path is shorter than vlimit·t′, we are responsible IFFour lateral velocity is greater than μ, in the direction of the hit.Disclosed is an algorithm for cautiousness verification with respect tooccluded pedestrians, which is described here in free pseudo code. Thecrucial part, that of checking existence of possibility of blamefulaccident with a pedestrian occluded by a vehicle, is done in the simplemanner described above.

Algorithm 2: Check cautiousness w.r.t. an occluded pedestrian for t′ ϵ:( ), t_(brake)]  Roll self future until t′  if Exists possibility ofblameful accident with a pedestrian occluded  by a vehicle   return“non-cautious” return “cautious”

On the Problem of Validating a Simulator

As previously discussed, multi-agent safety may be difficult to validatestatistically as it should be done in an “online” manner. One may arguethat by building a simulator of the driving environment, we can validatethe driving policy in the “lab.” However, validating that the simulatorfaithfully represents reality is as hard as validating the policyitself. To see why this is true, suppose that the simulator has beenvalidated in the sense that applying a driving policy π in the simulatorleads to a probability of an accident of {circumflex over (p)}, and theprobability of an accident of FC in the real world is p, with[p−{circumflex over (p)}]<∈. (We need that ∈ will be smaller than 10⁻⁹.)Next replace the driving policy to be π′. Suppose that with probabilityof 10⁻⁸, π′ performs a weird action that confuses human drivers andleads to an accident. It is possible (and even rather likely) that thisweird action is not modeled in the simulator, without contradicting itssuperb capabilities in estimating lie performance of the original policyπ. This proves that even if a simulator has been shown to reflectreality for a driving policy π, it is not guaranteed to reflect realityfor another driving policy.

The Lane-Based Coordinate System

One simplifying assumption that can be made in the RSS definition at theroad is comprised by adjacent, straight lanes, of constant width. Thedistinction between lateral and longitudinal axes, along with anordering of longitudinal position, may play a significant role in RSS.Moreover, the definition of those directions is clearly based on thelane shape. A transformation from (global) positions on the plane, to alane-based coordinate system reduces the problem to the original,“straight lane of constant width,” case.

Assume that the lane's center is a smooth directed curve r on the plane,where all of its pieces, denoted r⁽¹⁾, . . . , r_((k)), are eitherlinear, or an arc. Note that smoothness of the curve implies that nopair of consecutive pieces can be linear. Formally, the curve maps a“longitudinal” parameter, Y∈[Y_(min), Y_(max)]⊂

, into the plane, namely, the curve is a function of the form r:[Y_(min), Y_(max)]→

². We define a continuous lane-width function w: [Y_(min), Y_(max)]→

, mapping the longitudinal position Y into a positive lane width value.For each Y, from smoothness of r, we can define the normal unit-vectorto the curve at position Y, denoted r^(⊥)(Y). We naturally define thesubset of points on the plane which reside in the lane as follows:

R={r(Y)+aw(Y)r ^(⊥)(Y)Y∈[Y _(min) ,Y _(max)],α∈[±½]}

Informally, our goal is to construct a transformation ϕ of R into suchthat for two cars which are on the lane, their “logical ordering” willbe preserved: if c_(r) is “behind” c_(f) on the curve, thenϕ(c_(r))_(y)<ϕ(c_(f))_(y). If c_(t) is “to the left of” c_(r) on thecurve; then ϕ(c_(t)) <ϕ(c_(r))_(x). Where, as in RSS, we will associatethe y-axis with the “longitudinal” axis, and the x-axis with the“lateral”.

To define ϕ, we rely on the assumption that for all i, if r^((t)) is anarc of radius ρ, then the width of the lane throughout r_((t)) is ≤ρ/2.Note that this assumption holds for any practical road. The assumptiontrivially implies that for ail (x′,y′)∈R, there exists a unique pairY′∈[Y_(min), Y_(max)], α′∈[±½], s.t. (x′,y′)=r(Y′)+α′w(Y′)r^(⊥)(Y′). Wecan now define ϕ: R→

² to be ϕ(x′, y′)=(Y′, α′), where (Y′, α′) are the unique values thatsatisfy (x′, y′)=r(Y′)+α′w(r)r^(⊥)(Y′).

This definition captures the notion of a “lateral maneuver” in lane'scoordinate system. Consider, for example, a widening lane, with a cardriving exactly on one of the lane's boundaries (see FIG. 23). Thewidening of lane 2301 means that the car 2303 is moving away from thecenter of the lane, and therefore has lateral velocity with respect tothe lane. However, this doesn't mean it performs a lateral maneuver. Thedefinition of ϕ(x′, y′)_(x)=α′, namely, the lateral distance to thelane's center in w(Y′)-units, implies that the lane boundaries have afixed lateral position of ±½. Hence, a car that sticks to one of thelane's boundaries is not considered to perform any lateral movement.Finally, it can be seen that ϕ is a homomorphism. The term lane-basedcoordinate system is used when discussing ϕ(R)=[Y_(min), Y_(max)]×[±½],We have thus obtained a reduction from a general lane geometry to astraight, longitudinal/lateral, coordinate system.

Extending RSS to General Road Structure

in this section a complete definition of RSS that holds for all roadstructures is described. This section deals with the definition of RSSand not on how to efficiently ensure that a policy adheres to RSS. Theconcept of route priority is next introduced to capture any situation inwhich more than a single lane geometry exists, for example junctions.

The second generalization deals with two-way roads, in which there canbe two cars driving at opposite directions. For this case, the alreadyestablished RSS definition is still valid, with the minor generalizationof “safe distance” to oncoming traffic. Controlled junctions (that usetraffic lights to dictate the flow of traffic), may be fully handled bythe concepts of route priority and two-way roads. Unstructured roads(for example parking areas), where there is no clear route definitionmay also be handled with RSS. RSS is still valid for this case, wherethe only needed modification is a way to define virtual routes and toassign each car to (possibly several) routes.

Route Priority

The concept of route priority is now introduced to deal with scenariosin which there are multiple different road geometries in one scene thatoverlap in a certain area. Examples, as shown in FIGS. 24A-D, includeroundabouts, junctions, and merge into highways. A way to transformgeneral lane geometry into a lane-based one, with coherent meaning COI′longitudinal and lateral axes, has been described. Now scenarios inwhich multiple mutes of different road geometry exists are addressed. Itfollows that when two vehicles approach the overlap area, both perform acut-in to the frontal corridor of the other one. This phenomenon cannothappen when two routes have the same geometry (as is the case of twoadjacent highway lanes). Roughly speaking, the principle of routepriority states that if routes r₁, r₂ overlap, and r₁ has priority overr₂, then a vehicle coming from r₁ that enters into the frontal corridorof a vehicle that comes from r₂ is not considered to perform a cut-in.

To explain the concept formally, recall that the blame of an accidentdepends on geometrical properties which are derived from the lane'scoordinate system, and on worst case assumptions which rely on it too.Let r₁, . . . r_(k) be the routes defining the road's structure. As asimple example, consider the merge scenario, as depicted in FIG. 24A.Assume two cars, 2401 (c₁) and 2402 (c₂) are driving on routes r₁, r₂respectively, and r₁ is the prioritized mute. For example, suppose thatr₁ is a highway lane and r₂ is a merging lane. Having defined theroute-based coordinate systems for each route, a first observation isthat we can consider any maneuver in any route's coordinate system. Forexample, if we use r₂'s coordinate system, driving straight on r₁ seemslike a merge into r₂'s left side. One approach to definition of RSScould be that each of the cars can perform a maneuver IFF∀i∈{1, 2}, ifit is safe with respect to r₁. However, this implies that c₁, driving onthe prioritized route, should be very conservative w.r.t. r₂, themerging route, as c₂ can drive exactly on the route, and hence can winby lateral position. This is unnatural, as cars on the highway have theright-of-way in this case. To overcome this problem, we define certainareas in which route priority is defined, and only some of the routesare considered as relevant for safety,

Definition 22 (Accident Responsibility with Route Priority) Suppose r₁,r₂ are two routes with different geometry that overlap. We user₁>_([b, e]) r₂ to symbolize that r₁ has priority over r₂ in thelongitudinal interval [b, e] (FIG. 25) of r₁ coordinate system. Supposethere is on accident between cars c₁, c₂, driving on routes r₁, r₂. Fori∈{1, 2}, let b_(i)⊂{1, 2} indicate the cars to biome for the occidentwe consider the coordinate system of r₁. The blame for the accident isas follows:

-   -   if r₁>_([b,e]) r₂ and on the blame lime w.r.t. r₁, one of the        cars was in the interval [b,e] of the r₁-systems longitudinal        axis, then the blame is according to b₁.    -   Otherwise, the blame is according to b₁∪b2.

To illustrate the definition, consider again the merge into highwayexample. The fines denoted “b” and “e” in FIG. 25 indicate the values ofb, e for which r₁>_([b,e]) r₂. Thus, we allow cars to drive naturally onthe highway, while implying merging cars must be safe with respect tothose cars. In particular, observe that in the case a car 2401 c₁ drivesat the center of the prioritized lane, with no lateral velocity, it willnot be blamed for an accident with a car 2402 c₂ driving on anon-prioritized lane, unless 2402 c₂ has cut-in into 2401 c₁'s corridorat a safe distance. Note, that the end result is very similar to theregular RSS—this is exactly the same as a case where a car, on astraight road, tries to perform a lane change. Note that there may becases where the route used by another agent is unknown. For example, in26, car 2601 may not be able to determine whether a car 2602 will takepath “a” or path “b”. In such cases, RSS may be obtained by iterativelychecking all possibilities.

Two-Way Traffic

To deal with two-way traffic, the modification to the blame definitioncomes through sharpening the pails which rely on rear/frontrelationships, as those are of a slightly different meaning in suchcases. Consider two cars c₁, c₂ driving on some straight two lane road,in opposite longitudinal directions, namely, v_(1,long)·v_(2,long)<0.The direction of driving with respect to a lane may be negative inreasonable urban scenarios, such as a car deviating to the opposite laneto overtake a parked truck, or a car reversing into a parking spot. Itis therefore required to extend the definition of the safe longitudinaldistance which we have introduced for cases where negative longitudinalvelocity was assumed to be un-realistic. Recall that a distance betweenc_(r), c_(f) was safe if a maximal brake by c_(f) would allow enough ofresponse time for c_(r) to brake before crashing into c_(f). In ourcase, we again consider the “worst-case” by the opposite car, in aslightly different manner: of course we do not assume that the “worstcase” is that it speeds up towards us, but that it indeed will brake toavoid a crash—but only using some reasonable braking power. In order tocapture the difference in responsibility between the cars, when one ofthem clearly drives at the opposite direction, we start by defining a“correct” driving direction.

In the RSS definition for parallel lanes, the relevant lane has beendefined as the one whose center is closest to the cut-in position. Wecan now reduce ourselves to consideration of this lane (or, in the caseof symmetry, deal with the two lanes separately, as in Definition 22).In the definition below, the term “heading” denotes the arc tangent (inradians) of the lateral velocity divided by the longitudinal velocity.

Definition 23 ((μ₁, μ₂, μ₃)—Winning by Correct Driving Direction) Assumec₁, c₂ are driving in opposite directions, namelyv_(1,long)·v_(2,long)<0. Let x_(i), h_(i) be their lateral positions andheadings w.r.t. the lane. We say that c₁ (μ₁, μ₂, μ₃)—Wins by CorrectDriving Direction if all of the following conditions hold:

|h ₁|<μ₁,

|h ₂−π|<μ₂,

∥x ₁<μ₃.

The indicator of this event is denoted by W_(CDD) (i).

In words, c₁ wins if it drives close to the lane canter, in the correctdirection, while c₂

takes the opposite direction. At most one car can win, and it can bethat none of the cars does so. Intuitively, assume there is a crash inthe discussed situation. It is reasonable to put more responsibilityover a car c₁, that loses by Correct Driving Direction. This is done byre-defining a_(max,brake) for the case that a car wins by correctdriving direction.

Definition 24 (Reasonable Braking Power) Let a_(max,brake,wedd)>0 be aconstant, smaller than a_(max,brake). Assume c₁, c₂ are driving inapposite directions. The Reasonable Braking Power of each car c_(i),denoted RBA is a_(max,brake,wedd) if c₁ (μ₁, μ₂, μ₃)—Wins by CorrectDriving Direction and a_(max,brake) otherwise.

The exact values of a_(max, brake,wedd), a_(max,brake), for the cases ofwinning/not-winning by correct driving direction, are constants whichshould be defined, and can depend on the type of road and the lanesdriven by each car. For example, in a narrow urban street, it may be thecase that winning by a correct driving direction does not imply a muchlesser brake value: in dense traffic, we do expect a car to brake atsimilar forces, either when someone clearly deviated into its lane ornot. However, consider an example of a rural two way road, where highspeeds are allowed. When deviating to the opposite lane, cars whichdrive at the correct direction cannot be expected to apply a very strongbraking power to avoid hitting the host vehicle—the host vehicle willhave more responsibility than them. Different constants can be definedfor the case when two cars are at the same lane, with one of themreversing into a parking spot.

The safety distance between cars which are driving in oppositedirections, and immediately derive its exact value, is next defined.

Definition 25 (Safe Longitudinal Distance—Two-Way Traffic) Alongitudinal distance between a car c₁ and another car c₂ which aredriving in opposite directions and are both in the frontal corridors ofeach other, is safe w.r.t. a response time p if for any accelerationcommand a, |a|<a_(max,accel), performed by c₁, c₂ until time p, if c₁and c₂ will apply their Reasonable Braking Power from time p until afull stop then they won't collide.

Lemma 10 Let c₁, c₂ as in Definition 25. Let RBP_(h) a_(max,accel) bethe reasonable braking (for each i) and acceleration commands, and let pbe the cars' response tinge. Let v₁, v₂ be the longitudinal velocitiesof the cars, and let l₁, l₂ be their lengths. Definev_(i,p,max)=∥v_(i)|+ρ·a_(max,accel). Let L=(l_(r)+l_(f))/2. Then, theminimal safe longitudinal distance is:

$d_{\min} = {L + {\sum\limits_{i = 1}^{2}\left( {{\frac{\left| v_{i} \middle| {+ v_{i,{\rho.\max}}} \right.}{2}\rho} + \frac{v_{i,\rho,\max}^{2}}{2{RBP}_{i}}} \right)}}$

It can be seen that the term in the sum is the maximal distancetravelled by each car until it reaches full stop, when performing themaneuver from Definition 25. Therefore, in order for the full stop to beat a distance greater than L, the initial distance must be larger thanthis sum and an additional term of L.

The same blame time definition of RSS, with the non-safe longitudinaldistance as defined in Definition 25, is used to define theblame/accident responsibility for a two-way traffic scenario,

Definition 26 (Blame in Two-Way Traffic) The Blame in Two-Way Traffic ofan accident between cars c₁, c₂ driving in opposite directions, is afunction of the slate at the Blame Time, and is defined as follows:

-   -   If the Blame Time is also a cut-in time, the blame is defined as        in the regular RSS definition.    -   Otherwise, for every 1, the blame is on c_(i) if at some t that        happens after the blame time, c_(i) was not braking at a power        of at least RBP_(i).

For example, assume a safe cut-in occurred before the blame time. Forexample, c₁ has deviated to the opposite lane, performed a cut-in intoc₂'s corridor, at a safe distance. Note that c₂ wins by correct drivingdirection, and hence this distance can be very large—we do not expect c₂to perform strong braking power, but only the Reasonable Braking Power.Then, both cars have responsibility not to crash into each other.However, if the cut-in was not in a safe-distance, we use the regulardefinition, noting that c₂ will not be blamed if it drove in the centerof its lane, without lateral movement. The blame will be solely on c₁.This allows a car to drive naturally at the center of its lane, withoutworrying about traffic which may unsafely deviate into its corridor. Onthe other hand, safe deviation to the opposite lane, a common maneuverrequired in dense urban traffic, is allowed. Considering the example ofa car which initiates a reverse parking maneuver, it should startreversing while making sure the distance to cars behind it is safe.

Traffic Lights

In scenarios that include intersections with traffic lights, one mightthink that the simple rule for traffic lights scenarios is “if one car'sroute has the green light and the other car's route has a red light,then the blame is on the one whose route has the red light”. However,this is not the correct rule, especially in all cases. Consider forexample the scenario depicted in FIG. 27. Even if the ear 2701 is on aroute having a green light, we do not expect it to ignore car 2703 thatis already in the intersection. The correct rule is that the route thathas a green light has priority over routes that have a red light.Therefore, we obtain clear reduction from traffic lights to the routepriority concept we have described previously.

Unstructured Road

Turning to roads where no clear route geometry can be defined, considerfirst a scenario where there is no lane structure at all (e.g. a parkinglot). A way to ensure that there will be no accidents can be to requirethat every car will drive in a straight line, while if a change ofheading occurs, it must be done when there are no close cars in mysurrounding. The rationale behind this is that a car can predict whatother cars will do, and behave accordingly. If other cars deviate fromthis prediction (by changing heading), it is done with a long enoughdistance and therefore there may be enough time to correct theprediction. When there is lane structure, it may enable smarterpredictions on what other cars will do. If there is no lane structure atall, a car will continue according to its current heading. Technicallyspeaking, this is equivalent to assigning every car to a virtualstraight route according to its heading. Next, consider the scenario ina large unstructured roundabout (e.g., around the Arc de Triomphe inParis). Here, a sensible prediction is to assume that a car willcontinue according to the geometry of the roundabout, while keeping itsoffset. Technically, this is equivalent to assigning every car to avirtual are route according to its current offset from the center of theroundabout.

The above described driving policy system (e.g., the RL system) may beimplemented together with one or more of the described accidentliability rules to provide a navigational system that takes into accountpotential accident liability when deciding on a particular navigationalinstruction to implement. Such rules may be applied during the planningphase; e.g., within a set of programmed instructions or within a trainedmodel such that a proposed navigational action is developed by thesystem already in compliance with the rules. For example, a drivingpolicy module may account for or be trained with, for example, one ormore navigational rules upon which RSS is based. Additionally oralternatively, the RSS safety constraint may be applied as a filterlayer through which all proposed navigational actions proposed by theplanning phase are tested against the relevant accident liability rulesto ensure that the proposed navigational actions are in compliance. If aparticular action is in compliance with the RSS safety constraint, itmay be implemented. Otherwise, if the proposed navigational action isnot in compliance with the RSS safety constraint (e.g., if the proposedaction could result in accident liability to the host vehicle based onone or more of the above-described rules), then the action is not taken.

In practice, a particular implementation may include a navigation systemfor a host vehicle. The host vehicle may be equipped with an imagecapture device (e.g., one or more cameras such as any of those describedabove) that, during operation, captures images representative of anenvironment of the host vehicle. Using the image information, a drivingpolicy may take in a plurality of inputs and output a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The driving policy may include a set of programmedinstructions, a trained network, etc., that may receive various inputs(e.g., images from one or more cameras showing the surroundings of thehost vehicle, including target vehicles, roads, objects, pedestrians,etc.; output from LIDAR or RADAR systems; outputs from speed sensors,suspension sensors, etc.; information representing one or more goals ofthe host vehicle—e.g., a navigational plan for delivering a passenger toa particular location, etc.). Based on the input, the processor mayidentify a target vehicle in the environment of the host vehicle, e.g.,by analyzing camera images, LIDAR output, RADAR output, etc. In someembodiments, the processor may identify a target vehicle in theenvironment of the host vehicle by analyzing one or more inputs, such asone or more camera images, LIDAR output, and/or RADAR output. Further,in some embodiments, the processor may identify a target vehicle in theenvironment of the host vehicle based on an agreement of a majority orcombination of sensor inputs (e.g., by analyzing one or more cameraimages, LIDAR output, and/or RADAR output, and receiving a detectionresult identifying the target vehicle based on a majority agreement orcombination of the inputs).

Based on the information available to the driving policy module, anoutput may be provided in the form of one or more planned navigationalactions for accomplishing a navigational goal of the host vehicle. Insome embodiments, the RSS safety constraint may be applied as a filterof the planned navigational actions. That is, the planned navigationalaction, once developed, can be tested against at least one accidentliability rule (e.g., any of the accident liability rules discussedabove) for determining potential accident liability for the host vehiclerelative to the identified target vehicle. And, as noted, if the test ofthe planned navigational action against the at least one accidentliability rule indicates that potential accident liability may exist forthe host vehicle if the planned navigational action is taken, then theprocessor may cause the host vehicle not to implement the plannednavigational action. On the other hand, if the test of the plannednavigational action against the at least one accident liability ruleindicates that no accident liability would result for the host vehicleif the planned navigational action is taken, then the processor maycause the host vehicle to implement the planned navigational action.

In some embodiments, the system may test a plurality of potentialnavigational actions against the at least one accident liability rule.Based on the results of the test, the system may filter the potentialnavigational actions to a subset of the plurality of potentialnavigational actions. For example, in some embodiments, the subset mayinclude only the potential navigational actions for which the testagainst the at least one accident liability rule indicates that noaccident liability would result for the host vehicle if the potentialnavigational actions were taken. The system may then score and/orprioritize the potential navigational actions without accident liabilityand select one of the navigational actions to implement based on, forexample, an optimized score, or a highest priority. The score and/orpriority may be based, for example, one or more factors, such as thepotential navigational action viewed as being the safest, mostefficient, the most comfortable to passengers, etc.

In some instances, the determination of whether to implement aparticular planned navigational action may also depend on whether adefault emergency procedure would be available in a next state followingthe planned action. If a DEP is available, the RSS filter may approvethe planned action. On the other hand, if a DEP would not be available,the next state may be deemed an unsafe one, and the planned navigationalaction may be rejected. In some embodiments, the planned navigationalaction may include at least one default emergency procedure.

One benefit of the described system is that to ensure safe actions bythe vehicle, only the host vehicle's actions relative to a particulartarget vehicle need be considered. Thus, where more than one targetvehicle is present, the planned action for the host vehicle may betested for an accident liability rule sequentially with respect to thetarget vehicles in an influence zone in the vicinity of the host vehicle(e.g., within 25 meters, 50 meters, 100 meters, 200 meters, etc.). Inpractice, the at least one processor may be further programmed to:identify, based on analysis of the at least one image representative ofan environment of the host vehicle (or based on LIDAR or RADARinformation, etc.), a plurality of other target vehicles in theenvironment of the host vehicle and repeat the test of the plannednavigational action against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto each of the plurality of other target vehicles. If the repeated testsof the planned navigational action against the at least one accidentliability rule indicate that potential accident liability may exist forthe host vehicle if the planned navigational action is taken, then theprocessor may cause the host vehicle not to implement the plannednavigational action. If the repeated tests of the planned navigationalaction against the at least one accident liability rule indicate that noaccident liability would result for the host vehicle if the plannednavigational action is taken, then the processor may cause the hostvehicle to implement the planned navigational action.

As noted, any of the rules described above can be used as the basis forthe RSS safety test. In some embodiments, the at least one accidentliability rule includes a following rule defining a distance behind theidentified target vehicle within which the host vehicle nay not proceedwithout a potential for accident liability. In other cases, the at leastone accident liability rule includes a leading rule defining a distanceforward of the identified target vehicle within which the host vehiclemay not proceed without a potential for accident liability.

While the system described above can apply the RSS safety test to asingle planned navigational action to test compliance with the rule thatthe host vehicle should not take any action for which it would be liablefor a resulting accident, the test may be applied to more than oneplanned navigational action. For example, in some embodiments, the atleast one processor, based on application of at least one driving policymay determine two or more planned navigational actions for accomplishinga navigational goat of the host vehicle. In these situations, theprocessor may test each of the two or more planned navigational actionsagainst at least one accident liability rule for determining potentialaccident liability. And, for each of the two or more plannednavigational actions, if the test indicates that potential accidentliability may exist for the host vehicle if a particular one of the twoor more planned navigational actions is taken, the processor may causethe host vehicle not to implement the particular one of the plannednavigational actions. On the other hand, for each of the two or moreplanned navigational actions, if the test indicates that no accidentliability would result for the host vehicle if a particular one of thetwo or more planned navigational actions is taken, then the processormay identify the particular one of the two or more planned navigationalactions as a viable candidate for implementation. Next, the processormay select a navigational action to be taken from among the viablecandidates for implementation based on at least one cost function andcause the host vehicle to implement the selected navigational action.

Because an implementation of RSS relates to a determination of relativepotential liability for accidents between the host vehicle and one ormore target vehicles, along with testing planned navigational actionsfor safety compliance, the system may track accident liability potentialfor encountered vehicles. For example, not only may the system be ableto avoid taking an action for which a resulting accident would result inliability to the host vehicle, but the host vehicle systems may also beable to track one or more target vehicles and identify and track whichaccident liability rules have been broken by those target vehicles. Insome embodiments, an accident liability tracking system for a hostvehicle may include at least one processing device programmed toreceive, from an image capture device, at least one image representativeof an environment of the host vehicle and analyze the at least one imageto identify a target vehicle in the environment of the host vehicle.Based on analysis of the at least one image, the processor may includeprogramming to determine one or more characteristics of a navigationalstate of the identified target vehicle. The navigational state mayinclude various operational characteristics of the target vehicle, suchas vehicle speed, proximity to a center of a lane, lateral velocity,direction of travel, distance from the host vehicle, heading, or anyother parameter that may be used to determine potential accidentliability based on any or the rules described above. The processor maycompare the determined one or more characteristics of the navigationalstate of the identified target vehicle to at least one accidentliability rule (e.g., any of the rules described above, such as winningby lateral velocity, directional priority, winning by proximity to lanecenter, following or leading distance and cut-in, etc.). Based oncomparison of the state to one or more rules, the processor may store atleast one value indicative of potential accident liability on the partof the identified target vehicle. And in the case of an accident, theprocessor may provide an output of the stored at least one value (e.g.,via any suitable data interface, either wired or wireless). Such anoutput may be provided, for example, after an accident between the hostvehicle and at least one target vehicle, and the output may be used foror may otherwise provide an indication of liability for the accident.

The at least one value indicative of potential accident liability may bestored at any suitable time and under any suitable conditions. In someembodiments, the at least one processing device may assign and store acollision liability value for the identified target vehicle if it isdetermined that the host vehicle cannot avoid a collision with theidentified target vehicle.

The accident liability tracking capability is not limited to a singletarget vehicle, but rather can be used to track potential accidentliability fora plurality of encountered target vehicles. For example,the at least one processing device may be programmed to detect aplurality of target vehicles in the environment of the host vehicle,determine navigational state characteristics for each of the pluralityof target vehicles, and determine and store values indicative ofpotential accident liability on the part of respective ones of theplurality of target vehicles based on comparisons of the respectivenavigational state characteristics for each of the target vehicles tothe at least one accident liability rule. As noted, the accidentliability rules used as the basis for liability tracking may include anyof the rules described above or any other suitable rule. For example,the at least one accident liability rule may include a lateral velocityrule, a lateral position rule, a driving direction priority rule, atraffic light-based rule, a traffic sign-based rule, a route priorityrule, etc. The accident liability tracking function may also be coupledwith safe navigation based on RSS considerations (e.g., whether anyaction of the host vehicle would result in potential liability for aresulting accident).

In addition to navigating based on accident liability considerationsaccording to RSS, navigation can also be considered in terms of vehiclenavigational states and a determination of whether a particular, futurenavigational state is deemed safe (e.g., whether a DEP exists such thataccidents may be avoided or any resulting accident will not be deemedthe fault of the host vehicle, as described in detail above). The hostvehicle can be controlled to navigate from safe state to safe state. Forexample, in any particular state, the driving policy may be used togenerate one or more planned navigational actions, and those actions maybe tested by determining if the predicted future states corresponding toeach planned action would offer a DEP. If so, the planned navigationalaction or actions providing the DEP may be deemed safe and may qualifyfor implementation,

In some embodiments, a navigation system for a host vehicle may includeat least one processing device programmed to: receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle; determine, based on at least one driving policy, aplanned navigational action for accomplishing a navigational goal of thehost vehicle; analyze the at least one image to identify a targetvehicle in the environment of the host vehicle; test the plannednavigational action against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto the identified target vehicle; if the test of the plannednavigational action against the at least one accident liability ruleindicates that potential accident liability may exists for the hostvehicle if the planned navigational action is taken, then cause the hostvehicle not to implement the planned navigational action; and if thetest of the planned navigational action against the at least oneaccident liability rule indicates that no accident liability wouldresult for the host vehicle if the planned navigational action is taken,then cause the host vehicle to implement the planned navigationalaction.

In some embodiments, a navigation system for a host vehicle, may includeat least one processing device programmed to: receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle; determine, based on at least one driving policy, aplurality of potential navigational actions for the host vehicle;analyze the at least one image to identify a target vehicle in theenvironment of the host vehicle; test the plurality of potentialnavigational actions against at least one accident liability rule fordetermining potential accident liability for the host vehicle relativeto the identified target vehicle; select one of the potentialnavigational actions for which the test indicates that no accidentliability would result for the host vehicle if the selected potentialnavigational action is taken; and cause the host vehicle to implementthe selected potential navigational action. In some instances, theselected potential navigational action may be selected from a subset ofthe plurality of potential navigational actions for which the testindicates that no accident liability would result for the host vehicleif any of the subset of the plurality of potential navigational actionwere taken. Further, in some instances, the selected potentialnavigational action may be selected according to a scoring parameter.

In some embodiments, a system for navigating a host vehicle may includeat least one processing device programmed to receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle and determine, based on at least one driving policy, aplanned navigational action for accomplishing a navigational goal of thehost vehicle. The processor may also analyze the at least one image toidentify a target vehicle in the environment of the host vehicle;determine a next-state distance between the host vehicle and the targetvehicle that would result if the planned navigational action was taken;determine a current maximum braking capability of the host vehicle and acurrent speed of the host vehicle; determine a current speed of thetarget vehicle and assume a maximum braking capability of the targetvehicle based on at least one recognized characteristic of the targetvehicle; and implement the planned navigational action if, given themaximum braking capability of the host vehicle and current speed of thehost vehicle, the host vehicle can be stopped within a stopping distancethat is less than the determined next-state distance summed togetherwith a target vehicle travel distance determined based on the currentspeed of the target vehicle and the assumed maximum braking capabilityof the target vehicle. The stopping distance may further include adistance over which the host vehicle travels during a reaction timewithout braking.

The recognized characteristic of the target vehicle upon which themaximum braking capability of the target vehicle is determined mayinclude any suitable characteristic. In some embodiments, thecharacteristic may include a vehicle type (e.g., motorcycle, car, bus,truck, each of which may be associated with different braking profiles),vehicle size, a predicted or known vehicle weight, a vehicle model(e.g., that may be used to look up a known braking capability), etc.

In some cases, the safe state determination may be made relative to morethan one target vehicle. For example, in some cases a safe statedetermination (based on distance and braking capabilities) may be basedon two or more identified target vehicles leading a host vehicle. Such adetermination may be useful especially where information regarding whatis ahead of foremost target vehicle is not available. In such cases, itmay be assumed for purposes of determining a safe state, safe distance,and/or available DEP that the foremost detectable vehicle willexperience an imminent collision with an immovable or nearly immovableobstacle, such that the target vehicle following may reach a stop morequickly than its own braking profile allows (e.g., the second targetvehicle may collide with a first, foremost vehicle and therefore reach astop more quickly than expected max braking conditions). In such cases,it may be important to base the safe state, safe following distance, DEPdetermination upon the location of the foremost identified targetvehicle relative to the host vehicle.

In some embodiments, such a safe state to safe state navigation systemmay include at least one processing device programmed to receive; froman image capture device, at least one image representative of anenvironment of the host vehicle. Here, as with other embodiments, theimage information captured by an image capture device (e.g., a camera)may be supplemented with information obtained from one or more othersensors, such as a LIDAR or RADAR system. In some embodiments, the imageinformation used to navigate may even originate from a LIDAR or RADARsystem, rather than from an optical camera. The at least one processormay determine, based on at least one driving policy, a plannednavigational action for accomplishing a navigational goal of the hostvehicle. The processor may analyze the at least one image (e.g.,obtained from any of a camera, a RADAR, a LIDAR, or any other devicefrom which an image of the environment of the host vehicle may beobtained, whether optically based, distance map-based, etc.) to identifya first target vehicle ahead of the host vehicle and a second targetvehicle ahead of the first target vehicle. The processor may then determine a next-state distance between the host vehicle and the secondtarget vehicle that would result if the planned navigational action wastaken. Next, the processor may determine a current maximum brakingcapability of the host vehicle and a current speed of the host vehicle.The processor may implement the planned navigational action if, giventhe maximum braking capability of the host vehicle and the current speedof the host vehicle, the host vehicle can be stopped within a stoppingdistance that is less than the determined next-state distance betweenthe host vehicle and the second target vehicle.

That is, if the host vehicle processor determines that there is enoughdistance to stop in a next-state distance between the leading visibletarget vehicle and the host vehicle, without collision or withoutcollision for which responsibility would attach to the host vehicle andassuming the leading visible target vehicle will suddenly at any momentcome to a complete stop, then the processor of the host vehicle may takethe planned navigational action. On the other hand, if there would beinsufficient room to stop the host vehicle without collision, then theplanned navigational action may not be taken.

Additionally, while the next-state distance may be used as a benchmarkin some embodiments, in other cases, a different distance value may beused to determine whether to take the planned navigational action. Insome cases, as in the one described above, the actual distance in whichthe host vehicle may need to be stopped to avoid a collision may be lessthan the predicted next-state distance. For example, where the leading,visible target vehicle is followed by one or more other vehicles (e.g.,the first target vehicle in the example above), the actual predictedrequired stopping distance would be the predicted next-state distanceless the length of the target vehicle(s) following the leading visibletarget vehicle. If the leading visible target vehicle comes to animmediate stop, it may be assumed that the following target vehicleswould collide with the leading visible target vehicle and, therefore,they too would need to be avoided by the host vehicle to avoid acollision. Thus, the host vehicle processor can evaluate the next-statedistance less the summed lengths of any intervening target vehiclesbetween the host vehicle and the leading, visible/detected targetvehicle to determine whether there would be sufficient space to bringthe host vehicle to a hall under max braking conditions without acollision.

In other embodiments, the benchmark distance for evaluating a collisionbetween the host vehicle and one or more leading target vehicles may begreater than the predicted next-state distance. For example, in somecases, the leading visible/detected target vehicle may come to a quick,but not immediate stop, such that the leading visible/detected targetvehicle travels a short distance after the assumed collision. Forexample, if that vehicle hits a parked car, the colliding vehicle maystill travel some distance before coming to a complete stop. Thedistance traveled after the assumed collision may be less than anassumed or determined minimum stopping distance for the relevant targetvehicle. Thus, in some cases, the processor of the host vehicle maylengthen the next-state distance in its evaluation of whether to takethe planned navigational action. For example, in this determination, thenext-state distance may be increased by 5%, 10%, 20%, etc. or may besupplemented with a predetermined fixed distance (10 m, 20 m, 50 m,etc.) to account for a reasonable distance that the leading/visibletarget vehicle may travel after an assumed imminent collision.

In addition to lengthening the next-state distance in the evaluation byan assumed distance value, the next-state distance may be modified byboth accounting for a distance traveled after collision by the leadingvisible/detected target vehicle and the lengths of any target vehiclesfollowing the leading visible/detected target vehicle (which may beassumed to pile up with the leading visible/detected vehicle after itssudden stop).

In addition to basing the determination on whether to take the plannednavigational action on the next-state distance between the host vehicleand the leading visible/detected target vehicle (as modified byconsidering the post-collision movement of the leading visible/detectedtarget vehicle and/or the lengths of vehicles following the leadingvisible/detected target vehicle), the host vehicle may continue toaccount for the braking capability of one or more leading vehicles inits determination. For example, the host vehicle processor may continueto determine a next-state distance between the host vehicle and thefirst target vehicle (e.g., a target vehicle following the leadingvisible/detected target vehicle) that would result if the plannednavigational action was taken; determine a current speed of the firsttarget vehicle and assume a maximum braking capability of the firsttarget vehicle based on at least one recognized characteristic of thefirst target vehicle; and not implement the planned navigational actionif, given the maximum braking capability of the host vehicle and thecurrent speed of the host vehicle, the host vehicle cannot be stoppedwithin a stopping distance that is less than the determined next-statedistance between the host vehicle and the first target vehicle summedtogether with a first target vehicle travel distance determined based onthe current speed of the first target vehicle and the assumed maximumbraking capability of the first target vehicle. Here, as in the examplesdescribed above, the recognized characteristic of the first targetvehicle may include a vehicle type, a vehicle size, a vehicle model,etc.

In some cases (e.g., through actions of other vehicles), the hostvehicle may determine that a collision is imminent and unavoidable. Insuch cases, the processor of the host vehicle may be configured toselect a navigational action (if available) for which the resultingcollision would result in no liability to the host vehicle. Additionallyor alternatively, the processor of the host vehicle may be configured toselect a navigational action that would offer less potential damage tothe host vehicle or less potential damage to a target object than thecurrent trajectory or relative to one or more other navigationaloptions. Further, in some cases, the host vehicle processor may select anavigational action based on considerations of the type of object orobjects for which a collision is expected. For example, when faced witha collision with a parked car for a first navigational action or with animmovable object for a second navigational action, the action offeringthe lower potential damage to the host vehicle (e.g., the actionresulting in a collision with the parked car) may be selected. Whenfaced with a collision with a car moving in a similar direction as thehost vehicle fir a first navigational action or with a parked car for asecond navigational action, the action offering the lower potentialdamage to the host vehicle (e.g., the action resulting in a collisionwith the moving car) may be selected. When faced with a collision with apedestrian as a result of a first navigational action or with any otherobject for a second navigational action, the action offering anyalternative to colliding with a pedestrian may be selected.

In practice, the system for navigating a host vehicle may include atleast one processing device programmed to receive, from an image capturedevice, at least one image representative of an environment of the hostvehicle (e.g., a visible image, LIDAR image, RADAR image, etc.); receivefrom at least one sensor an indicator of a current navigational state ofthe host vehicle; and determine, based on analysis of the at least oneimage and based on the indicator of the current navigational state ofthe host vehicle, that a collision between the host vehicle and one ormore objects is unavoidable. The processor may evaluate availablealternatives. For example, the processor may determine, based on atleast one driving policy, a first planned navigational action for thehost vehicle involving an expected collision with a first object and asecond planned navigational action for the host vehicle involving anexpected collision with a second object. The first and second plannednavigational actions may be tested against at least one accidentliability rule for determining potential accident liability. If the testof the first planned navigational action against the at least oneaccident liability rule indicates that potential accident liability mayexist for the host vehicle if the first planned navigational action istaken, then the processor may cause the host vehicle not to implementthe first planned navigational action. If the test of the second plannednavigational action against the at least one accident liability ruleindicates that no accident liability would result for the host vehicleif the second planned navigational action is taken, then the processormay cause the host vehicle to implement the second planned navigationalaction. The objects may include other vehicles or non-vehicle objects(e.g., road debris, trees, poles, signs, pedestrians, etc.).

The following figures and discussion provide examples of variousscenarios that may occur when navigating and implementing the disclosedsystems and methods. In these examples, a host vehicle may avoid takingan action that would result in blame attributable to the host vehiclefor a resulting accident if the action is taken.

FIGS. 28A and 28B illustrate example following scenarios and rules. Asshown in FIG. 28A, the region surrounding vehicle 2804 (e.g., a targetvehicle) represents a minimum safe distance corridor for vehicle 2802(e.g., a host vehicle), which is traveling in the lane a distance behindvehicle 2804. According to one rule consistent with disclosedembodiments, to avoid an accident in which blame is attributable tovehicle 2802, vehicle 2802 must maintain a minimum safe distance byremaining in the region surrounding vehicle 2802. In contrast, as shownin FIG. 28B, if vehicle 2804 brakes, then vehicle 2802 will be at Faultif there is an accident.

FIGS. 29A and 29B illustrate example blame in cut-in scenarios. In thesescenarios, safe corridors around vehicle 2902 determine the fault incut-in maneuvers. As shown in FIG. 29A, vehicle 2902 is cutting in frontof vehicle 2902, violating the safe distance (depicted by the regionsurrounding vehicle 2902) and therefore is at fault. As show in FIG.29B, vehicle 2902 is cutting in front of vehicle 2902, but maintains asafe distance in front of vehicle 2904.

FIGS. 30A and 30B illustrate example blame in cut-in scenarios. In thesescenarios, safe corridors around vehicle 3004 determine whether vehicle3002 is at fault. In FIG. 30A, vehicle 3002 is traveling behind vehicle3006 and changes into the lane in which target vehicle 3004 istraveling. In this scenario, vehicle 3002 violates a safe distance andtherefore is at fault if there is an accident. In FIG. 30B, vehicle 3002cuts in behind vehicle 3004 and maintains a safe distance.

FIGS. 31A-31D illustrate example blame in drifting scenarios. In FIG.31A, the scenario starts with a slight lateral maneuver by vehicle 3104,cutting-in to the wide corridor of vehicle 3102. In FIG. 31B, vehicle3104 continues cutting into the normal corridor of the vehicle 3102,violating a safe distance region. Vehicle 3104 is to blame if there isan accident. In FIG. 31C, vehicle 3104 maintains its initial position,while vehicle 3102 moves laterally “forcing” a violation of ae normalsafe distance corridor. Vehicle 3102 is to blame if there is anaccident. In FIG. 31B, vehicle 3102 and 3104 move laterally towards eachother. The blame is shared by both vehicles if there is an accident.

FIGS. 32A and 32B illustrate example blame in two-way traffic scenarios.In FIG. 32A, vehicle 3202 overtakes vehicle 3206, and vehicle 3202 hasperformed a cut-in maneuver maintaining a safe distance from vehicle3204. If there is an accident, vehicle 3204 is to blame for not brakingwith reasonable force. In FIG. 32B, vehicle 3202 cuts-in without keepingsafe longitudinal distance from vehicle 3204. In case of an accident,vehicle 3202 is to blame.

FIGS. 33A and 333 illustrate example blame in two-way traffic scenarios.In FIG. 33A, vehicle 3302 drifts into the path of oncoming vehicle 3204,maintaining a safe distance. In case of an accident, vehicle 3204 is toblame for not braking with reasonable force. In FIG. 33B, vehicle 3202drifts into the path of the oncoming vehicle 3204, violating a safelongitudinal distance. In case of an accident, vehicle 3204 is to blame.

FIGS. 34A and 34B illustrate example blame in route priority scenarios.In FIG. 34A, vehicle 3202 runs a stop sign. Blame is attributed tovehicle 3202 for not respecting the priority assigned to vehicle 3204 bythe traffic light. In FIG. 34B, although vehicle 3202 did not havepriority, it was already in the intersection when vehicle 3204's lightturned green. If vehicle 3204 hits 3202, vehicle 3204 would be to blame.

FIGS. 35A and 35B illustrate example blame in route priority scenarios.In FIG. 35A, vehicle 3502 backing-up into the path of an oncomingvehicle 3504. Vehicle 3502 performs a cut-in maneuver maintaining a safedistance. In case of an accident, vehicle 3504 is to blame for notbraking with reasonable force. In FIG. 35B, vehicle 3502 car cuts-inwithout keeping a safe longitudinal distance. In case of an accident,vehicle 3502 is to blame.

FIGS. 36A and 36B illustrate example blame in route priority scenarios.In FIG. 36A, vehicle 3602 and vehicle 3604 are driving in the samedirection, while vehicle 3602 turns left across the path of vehicle3604. Vehicle 3602 performs cut-in maneuver maintaining safe distance.In case of an accident, vehicle 3604 is to blame for not braking withreasonable force. In FIG. 363, vehicle 3602 cuts-in without keeping safelongitudinal distance. In case of an accident, vehicle 3602 is to blame.

FIGS. 37A and 37B illustrate example blame in route priority scenarios.In FIG. 37A, vehicle 3702 wants to turn left, hut must give way to theoncoming vehicle 3704. Vehicle 3702 turns left, violating safe distancewith respect to vehicle 3704. Blame is on vehicle 3702. In FIG. 37B,vehicle 3702 turns left, maintaining a safe distance with respect tovehicle 3704. In case of an accident, vehicle 3704 is to blame for notbraking with reasonable force.

FIGS. 38A and 38B illustrate example blame in route priority scenarios.In FIG. 38A, vehicle 3802 and vehicle 3804 are driving straight, andvehicle 3802 has a stop sign. Vehicle 3802 enters the intersection,violating a safe distance with respect to vehicle 3804. Blame is onvehicle 3802. In FIG. 38B, vehicle 3802 enters the intersection whilemaintaining a safe distance with respect to vehicle 3804. In case of anaccident, vehicle 3804 is to blame for not braking with reasonableforce.

FIGS. 39A and 39B illustrate example blame in route priority scenarios.In FIG. 39A, vehicle 3902 wants to turn left, but must give way tovehicle 3904 corning from its right. Vehicle 3902 enters theintersection, violating the right-of-way and a safe distance withrespect to vehicle 3904. Blame is on vehicle 3902. In FIG. 39B, vehicle3902 enters the intersection while maintaining the right-of-way and asafe distance with respect to vehicle 3904. In case of an accident,vehicle 3904 is to blame for not braking with reasonable force.

FIGS. 40A and 40B illustrate example blame in traffic light scenarios.In FIG. 40A, vehicle 4002 is running a red light. Blame is attributed tovehicle 4002 for not respecting the priority assigned to vehicle 4004 bythe traffic light. In FIG. 40B, although vehicle 4002 did not havepriority, it was already in the intersection when the light for vehicle4004 turned green. If vehicle 4004 hits vehicle 4002, vehicle 4004 wouldbe to blame.

FIGS. 41A and 41B illustrate example blame in traffic light scenarios.Vehicle 4102 is turning left across the path of the oncoming vehicle4104. Vehicle 4104 has priority. In FIG. 41, vehicle 4102 turns left,violating a safe distance with respect to vehicle 4104. Blame isattributed to vehicle 4102. In FIG. 41B, vehicle 4102 turns left,maintaining a safe distance with respect to vehicle 4104. In case of anaccident, vehicle 4104 is to blame for not braking with reasonableforce,

FIGS. 42A and 42B illustrate example blame in traffic light scenarios.In FIG. 42A, vehicle 4202 is turning right, cutting into the path ofvehicle 4204, which is driving straight. Right-on-red is assumed to be alegal maneuver, but vehicle 4204 has right of way, as vehicle 4202violates a safe distance with respect to vehicle 4204. Blame isattributed to vehicle 4202. In FIG. 42B, vehicle 4202 turns right,maintaining a safe distance with respect to vehicle 4204. In case of anaccident, vehicle 4204 is to blame for not braking with reasonableforce.

FIGS. 43A-43C illustrate example vulnerable road users (VRUs) scenarios.Accidents with animals or VRUs where the vehicle performs a maneuver aretreated as a variation of a cut-in, where the default blame is on thecar, with some exceptions. In FIG. 43A, vehicle 4302 cuts into the pathof an animal (or VRU) while maintaining safe distance and ensuring anaccident can be avoided. In FIG. 43B, vehicle 4302 cuts into the path ofan animal (or VRU) violating safe distance. Blame is attributed tovehicle 4302. In FIG. 43C, vehicle 4302 notices the animal and stops,giving the animal sufficient time tit stop. If the animal hits the car,the animal is to blame.

FIGS. 44A-44C illustrate example vulnerable road users (VRUs) scenarios.In FIG. 44A, vehicle 4402 is turning left at a signalized intersectionand encounters a pedestrian in the crosswalk. Vehicle 4402 has a redlight and the VRU has a green. Vehicle 4402 is at fault. In FIG. 44B,vehicle 4402 has a green light, and the VRU has a red light. If the VRUenters the crosswalk, the VRU is at fault. In FIG. 44C, vehicle 4402 hasa green light, and the VRU has a red light. If the VRU was already inthe crosswalk, vehicle 4402 is it fault.

FIGS. 45A-45C illustrate example vulnerable road users (VRUs) scenarios,JR FIG. 45A, vehicle 4402 is turning right and encounters a cyclist. Thecyclist has a green light. Vehicle 4502 is at fault. In FIG. 45B, thecyclist has a red light. If the cyclist enters the intersection, thecyclist is at fault. In FIG. 45C, the cyclist has a red light, but wasalready in the intersection. Vehicle 4502 is at fault.

FIGS. 46A-46D illustrate example vulnerable road users (VRUs) scenarios.Accidents with VRUs where a vehicle does not perform performance amaneuver are blamed on the car by default, with some exceptions. In FIG.46A, vehicle 4602 must always make sure to maintain safe distance andensuring an accident can be avoided with a VRU. In FIG. 46B, if vehicle4602 does not maintain safe distance, vehicle 4602 is to blame. In FIG.46C, if vehicle 4602 does not maintain sufficiently low speed as toavoid colliding with a VRU that is potentially occluded by vehicle 5604,or drives above the legal limit, vehicle 4602 is to blame. In FIG. 46D,in another scenario with a potential occlusion of a VRU by vehicle 4604,if vehicle 4602 maintains sufficiently low speed, but the VRUs speed isabove a reasonable threshold, the VRU is to blame.

As disclosed herein, RSS defines a framework for multi-agent scenarios.Accidents with static objects, road departures, loss of control orvehicle failure are blamed on the host. RSS defines cautious maneuvers,which will not allow accidents with other objects, unless other objectsmaneuvers dangerously into the path of the host (in which case they areto blame). In the case of a sure-collision where blame is on the target,the host will apply its brakes. The system may consider evasive steeringonly if the maneuver is “cautious” (perceived not to cause anotheraccident).

Non-collision incidents include accidents initiated by vehicle fires,potholes, falling objects, etc. In these cases, the blame may default tothe host, except for scenarios which the host can avoid, such aspotholes and falling objects, which may be classified as a “staticobject” scenario, assuming they become visible at safe distance or thata cautious evasive maneuver exists. In multi-agent scenarios where thehost vehicle was stationary, the host is not to blame. In this case thetarget essentially performed a non-safe cut-in. For example, if acyclist rides into a stationary car, the host is not to blame.

RSS also includes guidelines for assigning blame where the road is notstructured clearly, such as parking lots or wide roundabouts withoutlane marks. In these unstructured road scenarios, blame is assigned byexamining deviations of each vehicle from its path to determine if theyallowed sufficient distance to allow other objects in the area toadjust.

Model for Safe and Scalable Self-Driving Vehicles

As previously discussed, a model called “Responsibility SensitiveSafety” (RSS) may formalize the notion of “accident blame.” RSS may beinterpretable and explainable, and may incorporate a sense of“responsibility” into the actions of a robotic agent.

In some embodiments, RSS is constructed by formalizing the followingfour rules: (1) keep a safe distance from the car in front, such that ifthe car in front brakes abruptly you will be able to stop in time; (2)keep a safe distance from cars on either side, and, when performinglateral maneuvers and cutting-in to another car's trajectory, leave theother car enough space to respond; (3) respect “right-of-way” rules,where “right-of-way” is given not taken; and (4) be cautious of occludedareas, for example, an area behind a parked car.

The discussion below presents a formalization of the above rules. Insome aspects, the formal model should satisfy soundness, e.g., when themodel says that the self-driving car is not responsible for an accident,the model should match the “common sense” of human judgement, andusefulness, e.g., a policy that guarantees to never cause accidentswhile still maintaining normal flow of traffic. In some embodiments, themodel assigns responsibility on the self-driving car in fuzzy scenarios,possibly resulting in extra cautiousness, as long as the model is stilluseful.

Satisfying each of these requirements, soundness and uniqueness,individually is trivial—a model that always assign responsibility to theself-driving car is sound but not useful, while a model that neverassign responsibility to the self-driving car is useful but not sound.Embodiments of the RSS model satisfy both soundness and usefulness.

Safe Distance

The first basic concept formalized in the discussion of RSS is that thetrailing car is always at fault if the trailing car hits a leading car.For example, two cars c_(f), C_(r), may be driving at the same speed,one behind the other, along a straight road, without performing anylateral maneuvers. Assume c_(f), the car at the front, suddenly brakesbecause of an obstacle appearing on the road, and manages to avoid it.Unfortunately, C_(r) did not keep enough of a distance from c_(f), isnot able to respond in time, and crashes into c_(f)'s rear side. In thisexample, the blame is on c_(r); it is the responsibility of the rear carto keep safe distance from the front car, and to be ready forunexpected, yet reasonable, braking.

The following definition formalizes the concept of a “safe distance.”

Definition 27 (Safe longitudinal distance same direction): Alongitudinal distance between a car c_(r) that drives behind another carc_(f), where both cars are driving at the same direction, is safe withrespect to a response time ρ for any braking of at most a_(max,brake)performed by c_(f), c_(r) will accelerate by, at most, a_(max,accel)during the response time and then will brake by at least a_(min,brake)until a full stop then it will not collide with c_(f).

In some embodiments, the safe longitudinal distance depends onparameters: ρ, a_(min,accel), a_(max,brake), a_(min,brake). Theseparameters may be determined, for example, by regulation. In someembodiments, the parameters are set differently for a robotic car and ahuman driven car. For example, the response time of a robotic car may besmaller than that of a human driver and a robotic car may brake moreeffectively than a typical human driver, hence a_(min, brake) may be alarger value for a robotic car than for a human-driven car. In otherembodiments, the parameters may be set differently for different roadconditions (wet road, ice, snow), which may be sensed, for example, byanalysis of images acquired from one or more onboard cameras, or basedon outputs from any other suitable sensors (e.g., windshield sensors,wheel slip sensors, etc.).

Lemma 11 below calculates the safe distance as a function of thevelocities of c_(r), c_(f) and the parameters in Definition 27.

Lemma 11: Let c_(r) be a vehicle which is behind c_(f) on thelongitudinal axis. Let ρ, a_(max,brake), a_(max,accel), a_(min,brake) beas in Definition 27. Let v_(r), v_(f) be the longitudinal velocities ofthe cars. Then, the minimal safe longitudinal distance between thefront-most point of c_(r) and the rear-most point of c_(f) is:

$d_{\min} = \left\lbrack {{v_{r}\rho} + {\frac{1}{2}a_{\max,{accel}}\rho^{2}} + \frac{\left( {v_{r} + {\rho a}_{\max,{accel}}} \right)^{2}}{2a_{\max,{brake}}} - \frac{v_{f}^{2}}{2a_{\max,{brake}}}} \right\rbrack_{+}$

Proof: Let d₀ denote the initial distance between c_(r) and c_(f).Denote v_(ρ,max)=v_(r)+ρa_(max, accel). The velocity of the front cardecreases with t at a rate a_(max, brake) (until arriving to zero orthat a collision happens), while the velocity of the rear car increasesin the time interval [0, ρ] (until reaching v_(p,max)) and thendecreases to zero e.g., a full stop or a collision) at a ratea_(min, brake)<a_(max, brake). It follows that if, at some point intime, the two cars have the same velocity, then from there on, the frontcar's velocity will be smaller, and the distance between them will bemonotonically decreasing until both cars reach a full stop (where the“distance” can be negative if collision happens). Thus, the worst-casedistance may happen either at time zero or when the two cars reach afull stop. In the former case, d₀>0. In the latter case, the distancesthe front and rear car will pass until a full stop may be

${{\frac{v_{f}^{2}}{a_{\max,{brake}}}\mspace{14mu} {and}\mspace{14mu} v_{r}\rho} + {\frac{1}{2}a_{\max,{accel}}\rho^{2}} + \frac{v_{\rho,\max}^{2}}{2a_{\min,{brake}}}},$

respectively. At that point (when both cars reach a full stop), thedistance between them should be larger than zero,

${d_{0} + \frac{v_{f}^{2}}{2a_{\max,{brake}}} - \left( {{v_{r}\rho} + {\frac{1}{2}a_{\max,{accel}}\rho^{2}} + \frac{v_{\rho,\max}^{2}}{2a_{\min,{brake}}}} \right)} > 0$

Rearranging terms yields Lemma 11, or the minimum safe distance.

The preceding definition of a safe distance may be sound for the casethat both the rear and front cars are driving at the same direction.Indeed, in this case, it is the responsibility of the rear car to keep asafe distance from the front car, and to be ready for unexpected, yetreasonable, braking. However, a definition is also needed for thescenario in which the two cars are driving in opposite directions.

Consider, for example, a car c_(r), that is currently at a safe distancefrom a preceding car, c_(f), that is stopped. Suddenly, c_(f) mayreverse into a parking spot, causing a collision with c_(r) from behind.Here, even though c_(r) hit c_(f) from behind, the responsibility is noton the rear car c_(r). To formalize this rule, the definitions of “rearand front” are defined so as not to apply to scenarios in which vehiclesare moving toward each other (namely, when the signs of theirlongitudinal velocities are opposite). In such cases, it may be expectedthat both cars decrease the absolute value of their velocities order toavoid a crash.

Thus, the safe distance between cars that drive in opposite directionsmay be defined as the distance required so that, if both cars brake(after a given response time), then no crash will occur. However, it maybe assumed that the car that drives in the opposite direction to thelane direction should brake harder than the one driving in the correctdirection. This leads to the following definition.

Definition 28 (Safe longitudinal distance—opposite directions: Considercars c₁, c₂ driving on a lane with longitudinal velocities v₁, v₂, wherev₂<0 and v₁≥0 (the sign of the longitudinal velocity is according to theallowed direction of driving on the lane). The longitudinal distancebetween the cars is safe with respect to a response time ρ, brakingparameters a_(min, brake), a_(min, brake, correct), and an accelerationparameter a_(max, accel), if in case c₁, c₂ will increase the absolutevalue of their velocities at rate a_(max, accel) during the responsetime, and from there on will decrease the absolute value of theirvelocities at rate a_(min, brake, correct), a_(min, brake),respectively, until a full stop, then there will not be a collision.

A calculation of the safe distance for the case of opposite directionsmay be given in the lemma below (whose proof is straightforward, andhence omitted).

Lemma 12: Consider the notation given in Definition 28. Definev_(1,ρ)=v₁+ρa_(max, accel) and v_(2,ρ)=|v₂|+ρa_(max, accel). Then, theminimal safe longitudinal distance between c₁ and c₂ is:

$d_{\min} = {{\frac{v_{1} + v_{1,\rho}}{2}\rho} + \frac{v_{a,p}^{2}}{2a_{\min,{brake},{correct}}} + {\frac{\left| v_{2} \middle| {+ v_{2,\rho}} \right.}{2}\rho} + \frac{v_{2,\rho}^{2}}{2a_{\min,{brake}}}}$

Before a collision between two cars, the cars must first be at anon-safe distance.

Intuitively, the idea of the safe distance definitions is that if bothcars will respond “properly” to violations of the safe distance thenthere cannot be a collision. If one of them does not respond “properly”then that care is responsible for the accident. To formalize this, it isfirst important to define the moment just before the cars start to be ata non-safe distance.

Definition 29 (Dangerous Longitudinal Situation and Blame Time): Lettime t be dangerous for cars c₁, c₂ if the distance between them at timet is non-safe (according to Definition 27 or Definition 28). Given adangerous time t, its Blame Time, denoted t_(b), is the earliestnon-dangerous time such that all the times in the interval (t_(b), t]are dangerous. For example, an accident can only happen at time t if itis dangerous, and thus the blame time of the accident is the blame timeof t.

Definition 30 (Proper response to dangerous longitudinal situations): Asabove, let t be a dangerous time for cars c₁, c₂ and let t_(b) be thecorresponding blame time. Assume the two cars comply with the followingconstraints on the longitudinal speed:

-   -   1. First, for example; if at the blame time, the two cars were        driving at the same direction, and say that c₁ is the rear car,        then        -   c₁ acceleration must be at most a_(max, accel) during the            interval [t_(b), t_(b)+ρ) and at most −a_(min, brake) from            time t_(b)+ρ until reaching a full stop, after which any            non-positive acceleration is allowed. In other words, the            following car is allowed to accelerate at a rate up to its            maximum acceleration capability (e.g., full throttle level)            during the reaction time period, but then, must decelerate            at a rate associated with a braking rate between a selected            minimum braking rate for the car and the ear's maximum            braking rate. The selected minimum braking rate may be            regulation dependent or selected based on any other suitable            criteria.        -   c₂ acceleration must be at least −a_(max, brake) until            reaching a full stop, after which, any non-negative            acceleration is allowed. That is, the leading car is allowed            to decelerate at a rate up to a deceleration rate associated            with the leading car's maximum braking capability.    -   2. Second, if at the blame time the two cars were driving at        opposite directions, and, for example, c₂ was driving in the        wrong direction (e.g., c₂ has a negative velocity), then:        -   c₁ acceleration must be at most a_(max, accel) during the            interval [t_(b), t_(b)+ρ) and at most            −a_(min, brake, correct) from time t_(b)+ρ until reaching a            full stop, after which any non-positive acceleration is            allowed. Car c₁ may accelerate toward car c₂ at a maximum            acceleration capability during the reaction time, but then,            must decelerate at a rate associated with a braking rate            between a selected minimum braking rate fir the car and the            car's maximum braking rate. The selected minimum braking            rate may be regulation dependent or selected based on any            other suitable criteria.        -   c₂ acceleration must be at least −a_(max, accel) during the            interval [t_(b), t_(b)+ρ) and at most a_(min, brake) from            time t_(b)+ρ until reaching a fill(stop, after which any            non-negative acceleration is allowed. In other words, car c₂            may accelerate toward car c₁ at a rate up to a maximum            acceleration rate for car c₂ during car c₂'s reaction time.            After that, car c₂ must decelerate at a rate associated with            a braking rate between a selected minimum braking rate for            the car and the car's maximum braking rate. The selected            minimum braking rate may be regulation dependent or selected            based on any other suitable criteria. Additionally, the            selected minimum braking rate of car c₂ may be different            than the selected minimum braking rate of car c₁ (e.g., the            minimum braking rate that must be applied by the car driving            in the incorrect direction may be higher than the minimum            braking rate required of the car driving in the correct            direction).

As mentioned previously, assume that collisions can only happen atdangerous times. Thus, if once the distance between cars become non-safethey both apply their “proper response to dangerous situations” from thecorresponding blame time (until the distance between them becomes safeagain) then collision cannot happen. Hence the responsibility foraccidents may be assigned to the agent(s) that did not respond properlyto the dangerous situation preceding the collision. In some embodiments,the definition below may apply to scenarios in which no lateralmaneuvers are performed (that is, each car keeps its lateral position inthe lane).

In the next section, the definition may be extended to the case in whichcars can perform lateral maneuvers.

Definition 31 (Responsibility for an Accident—no lateral maneuvers):Consider an accident between c₁ and c₂ at time t and let t_(b) be thecorresponding blame time. Car c₁ is responsible for the accident if itdid not follow the constraints defined by the “proper response todangerous situations” (Definition 30) at some time in the interval(t_(b), t].

Additionally, it may be possible that both c₁ and c₂ share theresponsibility for an accident (e.g., if both of them did not complywith the proper response constraints).

Responsibility in Lateral Maneuvers

In some embodiments, the RSS model may formally define responsibilitywhen cars are performing lateral maneuvers. A first example assumes astraight road on a planar surface, where the lateral, longitudinal axesare the x, y axes, respectively. For example, as discussed above withreference to the lane-based coordinate system. In some embodiments, thelongitudinal and lateral velocities may be the derivatives of thelongitudinal and lateral positions on the straight virtual road obtainedby a bijection between the actual curved road and a straight road.Similarly, accelerations may be second derivatives of positions.

Unlike longitudinal velocity, which may be kept at a value of 0 for longperiods offline (e.g., when the car is not moving), keeping lateralvelocity at exact 0 may be difficult as cars usually perform smalllateral fluctuations. Thus, the model may introduce a robust notion oflateral velocity.

Definition 32 (μ-lateral-velocity): Consider a point located at alateral location l at time t. Its u-lateral velocity at time t isdefined as follows. Let t_(out)>t be the earliest future time at whichthe point's lateral position, denoted l_(out), is either

$1 - {\frac{\mu}{2}\mspace{14mu} {or}\mspace{14mu} 1} + \frac{\mu}{2}$

(if no such time exists let t_(out)=∞). If at some time t′∈(t, t_(out))the point's lateral position is 1, then the p-lateral-velocity is 0.Otherwise, the μ-lateral-velocity is

$\frac{l_{out} - l}{t_{out} - t}.$

In some embodiments, in order to have a collision between two vehicles,it is required that they are close in proximity both longitudinally andlaterally. A safe longitudinal distance has been defined above.

Definition 33 (Safe Lateral Distance): The lateral distance between carsc₁, c₂ driving with lateral velocities v₁, v₂ is safe with respect toparameters ρ, a_(min, brake) ^(lat), a_(max, accel) ^(lat), μ if duringthe time interval [0, ρ] the two cars will apply lateral acceleration ofa_(max, accel) ^(lat) toward each other, and after that the two carswill apply lateral braking of a_(min, brake) ^(lat), until each carreaches zero lateral velocity, then the final lateral distance betweenthem will be at least μ.

A calculation of the lateral safe distance may be given in the lemmabelow.

Lemma 13: Consider the notation given in Definition 33. Without loss ofgenerality, assume that c₁ is to the left of c₂. Definev_(1,ρ)=v₁+a_(max, accel) ^(lat) and v_(2,ρ)=v₂−a_(max, accel) ^(lat).Then, the minimal safe lateral distance between the right side of c₁ andthe left part of c₂ is:

$d_{\min} = {\mu + \left\lbrack {{\frac{v_{1} + v_{1,\rho}}{2}\rho} + \frac{v_{1,\rho}^{2}}{2a_{\min,{brake}}^{lat}} - \left( {{\frac{v_{2} + v_{2,\rho}}{2}\rho} - \frac{v_{2,\rho}^{2}}{2a_{\min,{brake}}^{lat}}} \right)} \right\rbrack_{+}}$

As previously mentioned, in order to have a collision between two cars,assume the cars must be both at a non-safe longitudinal distance and ata non-safe lateral distance. Thus, the idea of the safe distancedefinitions is that if both cars respond “properly” to violations ofsafe distance then there cannot be a collision. If one car did notrespond “properly” then that car is responsible for the accident. Inthis example, the model may use modified definitions of DangerousSituation and Blame Time.

Definition 34 (Dangerous Situation and Blame Time): Let time t bedangerous for cars c₁, c₂ if both the longitudinal and lateral distancesbetween them are non-safe (according to Definition 27, Definition 28,and Definition 33). Given a dangerous time t, its Blame Time, denotedt_(b), is the earliest non-dangerous time such that all the times in theinterval {t_(b), t] are dangerous. In this example, an accident may onlyhappen at time t if it is dangerous, and in that case the blame time ofthe accident is the blame time of t.

Definition 35 (Proper response to dangerous situations): Let t be adangerous time for cars c₁, c₂ and let t_(b) be the corresponding blametime. Assume the proper behavior of the two cars is to comply with thefollowing constraints on the lateral/longitudinal speed:

-   -   1. If before the blame time there was a safe longitudinal        distance between c₁ and c₂ then the longitudinal speed is        constrained according to Definition 30.    -   2. If before the blame time there was a safe lateral distance        between c₁ and c₂, and without loss of generality, assuming that        at that time c₁ was to the left of c₂:        -   if t 0 [t_(b), t_(b)+ρ) then both cars can do any lateral            action as long as their lateral acceleration, a, satisfies            |a|≤a_(max, accel) ^(lat).        -   Otherwise, if t>t_(b)+ρ:            -   then before reaching p-lateral-velocity of 0, c₁ must                apply lateral acceleration of at most −a_(min, brake)                ^(lat) and c₂ must apply lateral acceleration of at                least a_(min, brake) ^(lat). In other words, c₁ must                have at least a minimum lateral acceleration in one                direction, and c₂ must have at least a minimum lateral                acceleration in the opposite direction.            -   After reaching μ-lateral-velocity of 0, c₁ may have any                non-positive μ-lateral-velocity and c₂ may have any                non-negative p-lateral-velocity    -   3. Minimal evasive effort: in addition to the rules above, the        following constraints may apply.        -   First, in the case of item (1) above: Suppose that at the            blame time the two cars are driving at the same direction            and c₂ is the car on the front. Then, after time t_(b)+ρ and            until reaching a μ-lateral-velocity of 0, it should brake            laterally by at least a_(min, brake, evasive) ^(lat). And,            after that it should stay at μ-lateral-velocity of 0.        -   In case of item (2) above: Suppose that c₁ responds properly            until reaching a lateral-velocity of 0, and curing that time            c₂ did not respond properly and is now in front of c₁            (namely, all points of c₂ are longitudinally in front of all            points of c₁, and some point of c₂ is at the same lateral            position of some point of c₁). Let the first moment that            this happens, the cut-in time, be denoted t_(c). Then, if            t_(b)<t_(c)<t−ρ and currently c₁'s velocity is positive,            then c₁ must brake longitudinally at a rate of at least            a_(min, brake, evasive).

In the above definition, all but the item titled “Minimal evasiveeffort” capture the essence of the assumptions in the definitions ofsafe distance, in the sense that if both cars respond properly thenthere will no collision. The “Minimal evasive effort” deals with casesin which extra caution is applied to prevent potential situations fromarising in which responsibility might be shared. For example, when therear car, c₁, should keep a safe distance from the front car, c₂, and c₂is overly cautious and avoids lateral maneuvers so as to preventcollisions in case c₁ will not brake strong enough. The second case iswhen, for example, c₂ performs a cut-in, at a non-safe longitudinaldistance, while c₁ was behaving properly. In this case, c₂ did notbehave correctly. Nevertheless, c₁ is expected to make an effort toavoid a potential collision, for example, by applying braking of atleast a_(min, brake, evasive). This may reduce the duration of adangerous situation (unless both cars are at a zero longitudinal andlateral velocity).

Definition 36 (Responsibility for an Accident): Consider, for example,an accident between c₁ and c₂ at time t and let t_(b) be thecorresponding Blame Time. Car c may be responsible for the accident ifit did not respond properly according to Definition 35 at some time in(t_(b), t], as illustrated in FIG. 47A.

In FIG. 47A, the vertical lines around each car show the possiblelateral position of the car if it will accelerate laterally during theresponse time and then will brake laterally. Similarly, the rectanglesshow the possible longitudinal positions of the car (e.g., if the careither brakes by a_(max,brake) or accelerates during the response timeand then will brake by a_(min,brake)). In the top two rows (rows a andb), before the blame time there was a safe lateral distance, hence theproper response is to brake laterally. The yellow car is already atμ-lateral-velocity of zero, hence only the red car brakes laterally. Inthe third row (row c), before the blame time there was a safelongitudinal distance, hence the proper response is for the car behindto brake longitudinally. Finally, in the fourth row (row d), before theblame time there was a safe longitudinal distance, in an oncomingscenario, hence both car should brake longitudinally.

The parameters a_(max,accel) ^(lat), a_(max,accel), and a_(max,brake) donot necessarily reflect a physical limitation, but instead they mayrepresent an upper bound on reasonable behavior expected from roadusers. In some embodiments, based on these definitions, if a driver doesnot comply with these parameters at a dangerous time be immediatelybecomes responsible for the accident.

For simplicity, assume that cars can immediately switch from applying a“lateral braking” of a_(min,brake) ^(lat) to being at ap-lateral-velocity of 0. This may not always be possible due to physicalproperties of the car. However, the important factor in the definitionof proper response is that from time t_(b)+ρ to the time the car reachesa p-lateral-velocity of 0, the total lateral distance it will pass willnot be larger than the one it would have passed had it applied a brakingof a_(min,brake) ^(lat) until a full stop. In some embodiments,achieving this goal by a real vehicle is possible by first braking at astronger rate and then decreasing lateral speed more gradually at theend. In some embodiments, this change in the braking rate may not affectthe RSS model.

In some embodiments, the definitions above hold for vehicles ofarbitrary shapes, by taking the worst-case with respect to all points ofeach car. For example, the model may account for semi-trailers or a carwith an open door.

Multiple Geometry and Right-of-Way Rules

In some scenarios, there may be multiple different road geometries inone scene, or environment, that overlap in a certain area. FIG. 47Bshows exemplary road geometries including a roundabout 4706, junctions4704 and 4708, and merges onto highways 4702. In many such cases, oneroute, shown in solid line, may have priority over others, shown indashed line, and vehicles riding on that route have the right of way.

When facing scenarios of multiple route geometries, the abovedefinitions may need to be adjusted. For example, consider theT-junction 4702 depicted in FIG. 478, and suppose that there is a stopsign for the route denoted by the solid line. Suppose that c₁ isapproaching the intersection on the dashed route and at the same time c₂is approaching the intersection on the solid mute. According to thedashed route's coordinate system, c₂ has a very large lateral velocity,hence c₁ might deduce that c₂ is already at a non-safe lateral distance,which implies that c₁, driving on the prioritized route, must reducespeed in order to maintain a safe longitudinal distance to c₂. Thismeans that c₂ should be very conservative with respect to traffic thatcoming from the solid route. This is of course an unnatural behavior, ascars on the yellow route have the right-of-way in this case.Furthermore, even c₂, who doesn't have the priority, should be able tomerge into the junction as long as c₁ can stop in time (this will becrucial in dense traffic). This example shows that when c₁ drives on r₁,it doesn't make sense to consider its position and velocity w.r.t thecoordinate system of r₂. As a result, the preceding concepts such as“what does it mean that c₁ is in front of c₂”, and what does it mean tobe at a non-safe distance may be generalized.

In the case of multiple geometries, the definition of safe lateraldistance may be generalized. Applying the definition below to two routesof the same geometry may yield the same definition as in Definition 33.As referred to herein, a route may be a subset of R². Further, assumethat two cars in the examples below, c₁, c₂ are driving on differentroutes, r₁, r₂. In some situations (for example, the T-junction 4704given in FIG. 47B), once there is exactly a single route r₁ such thatboth cars are assigned to the route, and the time is not dangerous, thenfrom that moment on, the definitions are described solely with referenceto r₁.

Definition 37 (Lateral Safe Distance for Two Routes of DifferentGeometry): Consider, for example, vehicles c₁, c₂ driving on routes r₁,r₂ that intersect. For every i∈{1, 2}, let [x_(i,min), x_(i,max)] be theminimal and maximal lateral positions in r_(i) that c_(i) can be in, ifduring the time interval [0, ρ) the car applies a lateral acceleration(with respect to r_(i)), |z^(lat)|≤a_(max,accel) ^(lat), and after thatapplies a lateral braking of at least a_(min,brake) ^(lat) (again withrespect to r_(i)), until reaching a zero lateral velocity (with respectto r_(i)). The lateral distance between c₁ and c₂ is safe if therestrictions of r₁, r₂ to the lateral intervals [x_(1,min), x_(1,max)],[x_(2,min), x_(2,max)] are at a distance of at least μ. Where therestriction of r_(i) to the lateral intervals [x_(1,min), x_(i,max)] maybe the subset of R² obtained by all points (x, y)∈r₁ for which thesemantic lateral position of (x, y) is in the interval [x_(i,min),x_(i,max)].

Definition 38, below, is an exemplary quantification of the orderingbetween two cars when no common longitudinal axis exists (e.g., if thecars are not driving one in front of the other).

Definition 38 (Longitudinal Ordering for Two Routes of DifferentGeometry): Consider, for example, c₁, c₂, 4710 and 4712, respectively,driving on routes r₁, r₂, 4714 and 4716, respectively, that intersect asshown in FIG. 47C. For example, c₁ (vehicle 4710) is longitudinally infront of c₂ (vehicle 4712) if either of the following holds: for everyi, if both vehicles are on r_(i) then c₁ is in front of c₂ according tor_(i); or c₁ is outside r₂ and c₂ is outside r₁, and the longitudinaldistance from c₁ to the set r₁∩r₂, with respect to r₁, is larger thanthe longitudinal distance from c₂ to the set r₁∩r₂, with respect to r₂.

As a measure of robustness of the longitudinal ordering definition, forexample, suppose that c₁, c₂ are at distances of 20, 20.1 meters,respectively, from the intersection. The definition holds because thedefinition is effectively being used only when there is a safelongitudinal distance between the two cars, and, thus, the orderingbetween the cars will be obvious. Furthermore, this situation isanalogous to the non-robustness of ordering when two cars are drivingside by side on a multi-lane highway road.

Definition 39 (Longitudinal Safe Distance for Two Routes of DifferentGeometry): Consider, for example, c₁, c₂ driving on routes r₁, r₂ thatintersect. The longitudinal distance between c₁ and c₂ is safe if one ofthe following holds:

-   -   1. If for all i∈{1, 2} such that r_(i) has no priority, if c_(i)        will accelerate by a_(max,accel) for ρ seconds, and will then        brake by a_(min,brake) until reaching zero longitudinal velocity        (all respect to r_(i)), then during this time c_(i) will remain        outside of the other route.    -   2. Otherwise, if c₁ is in front of c₂ (according to Definition        38), then the cars are at a safe longitudinal distance. For        example, if c₁ brakes by a_(max,brake) until reaching a zero        velocity (with respect to r₁), and c₂ accelerates by at most        a_(max,accel) for ρ seconds and then brakes by at least        a_(min,brake) (with respect to r₂) until reaching a zero        velocity, then c₁ will remain in front of c₂ (according to        Definition 38).    -   3. Otherwise, consider a point p∈r₁∩r₂ such that for i∈{1, 2},        the lateral position of p with respect to r_(i) is in        [x_(1,min), x_(1,max)] (as defined in Definition 37). Let        [t_(i,min), t_(i,max)] be all times such that c_(i) can arrive        to the longitudinal position of p with respect to r₁ if it will        apply longitudinal accelerations in the range [−a_(max,brake),        a_(max,accel)] during the first ρ seconds, and then will apply        longitudinal braking in the range [a_(min,brake), a_(max,brake)]        until reaching a zero velocity. Then, the vehicles may be at a        safe longitudinal distance if for every such p, [t_(1,min),        t_(1,max)] does not intersect [t_(2,min), t_(2,max)].

FIG. 47D is an exemplary illustration of Definition 39. Frame 4720 is anexemplary safe situation in which car 4722 has priority because car 4724must stop prior to entering the roadway. Frame 4726 is another exemplarysafe situation in which car 4722 is in front of car 4724, thus givingcar 4724 time to stop if car 4722 stops or slows. In frame 4728, If car4722 is at a full stop and car 4724 is at a full lateral stop, thesituation is safe by the definition of item (3) of Definition 39.

Definition 40 (Dangerous & Blame Times, Proper Response, andResponsibility for Routes of Different Geometry): Consider, for example,vehicles c₁, c₂ driving on routes r₁, r₂. Time t may be dangerous ifboth the lateral and longitudinal distances are non-safe (according toDefinition 11 and Definition 13). The corresponding blame time may bethe earliest non-dangerous time is such that all times in (t_(b), t] aredangerous. The proper response of c₁ and/or c₂ may depend on thesituation immediately before the blame time:

-   -   If the lateral distance was safe, then both cars should respond        according to the description of lateral safe distance in        Definition 37.    -   Else, if the longitudinal distance was safe according to        item (1) in Definition 39, then if a vehicle is on the        prioritized route it can drive normally, and otherwise it must        brake by at least a_(min,brake) if t−t_(b)≥ρ.    -   Else, if the longitudinal distance was safe according to        item (2) in Definition 39, then c₁ can drive normally and c₂        must brake by at least a_(min,brake) if t−t_(b)≥ρ.    -   Else, if the longitudinal distance was safe according to        item (3) in Definition 39, then both cars can drive normally if        t−t_(b)<ρ, and otherwise, both cars should brake laterally and        longitudinally by at least a_(min,brake) ^(lat, a) _(min,brake)        (each one with respect to its own route).

Finally, if a collision does occur, then the responsibility nay be onthe vehicle(s) that did not comply with the proper response. In someembodiments, there are cases where the route used by another agent isunknown: for example, in FIG. 47E. In FIG. 47E, at the path of car 4730at the intersection is unknown to car 4732. In such case, RSS may beobtained by checking all possibilities.

Traffic Lights

In some embodiments, a vehicle may encounter a situation involving atraffic light. It may not hold that “if one car's route has the greenlight and the other car's route has a red light, then the blame is onthe one whose route has the red light.” Rather, consider for example thescenario depicted in FIG. 47F. Even if the car 4734's route has a greenlight, it is not expected it to ignore car 4736 that is already in theintersection. The route that has a green light may have a priority overroutes that have a red light. Therefore, the concept of a situation witha traffic light reduces to the route priority situation previouslydescribed. In some embodiments, the rule for route priority may besimplified conceptually as the right of way is given, not taken.

Unstructured Road

In some embodiments, a vehicle may encounter unstructured roads, forexample, as shown in FIG. 47G. Consider first the scenario 4718. Here,while the partition of the road area to lanes is not well defined, thepartition of the road to multiple routes (with a clear geometry forevery route) is well defined. Since our definitions of responsibilityonly depend on the route geometry, they apply as is to such scenarios.

Next, consider the scenario where there is no route geometry at all(e.g. the parking lot 4738). Unlike the structured case, lateral andlongitudinal directions are separated, this scenario requirestwo-dimensional trajectories.

Definition 41 (Trajectories): Consider, for example, a vehicle c ridingon some road. A future trajectory of c may be represented as a functionτ: R⁺→R², where τ (t) is the position of c in t seconds from the currenttime. The tangent vector to the trajectory at t, denoted τ (t), is theJacobian of τ at t. Denoting t_(s)(τ)=sup{t: ∀t_(l)∈[0, t),∥τ′(t_(l))∥>0}, namely, that t_(s) is the first time in which thevehicle will arrive to a full stop, where if no such t exists, sett_(s)(τ)=∞.

Dangerous situations may be identified based on the possibility of acollision between two trajectories, as described with reference toDefinition 42.

Definition 42 (Trajectory Collision): Let τ₁, τ₂ be two futuretrajectories of c₁, c₂, with corresponding stopping times t₁=t_(s)(τ₁),t₂=t_(s)(τ₂). Given parameters ǫ, θ, then τ₁ and τ₂ do not collide,which may be denoted by τ₁∩τ₂=Ø, if either of the following holds:

-   -   1. For every t∈[0, max(t₁, t₂)] then ∥τ₁(t)−τ₂(t)∥>ϵ.    -   2. For every t∈[0, t₁] then ∥τ₁(t)−τ₂(t)∥>ϵ and the absolute        value of the angle between the vectors (τ₂(t₁)−τ₁(t₁)) and        τ₂(t₁) is at most θ.

Given a set of trajectories for c_(i), denoted T₁, and a set oftrajectories for c₂, denoted T₂, then T₁∩T₂=Ø if for every (τ₁,τ₂)∈T₁×T₂ then τ₁∩τ₂=Ø.

The first item states, for example, that both vehicles will be away fromeach other until they are both at a full stop. The second item states,for example, that the vehicles will be away from each other until thefirst one is at a full stop, and at that time, the velocity vector ofthe second one points away from the first vehicle.

In some embodiments, the collision operator may not be commutative. Forexample, assume two cars are currently driving on a large circle in thesame direction, where c₁ is closely behind c₂, and consider τ₁ to be thetrajectory in which c₁ brakes strongly and τ₂ is the trajectory in whichc₂ continues at the same speed forever. Then, τ₁∩τ₂=Ø while τ₂∩τ₁/=Ø.

In some embodiments, abstract notions of “braking” and “continueforward” behaviors may be assumed. In the structured case, the meaningsof these behaviors may be defined based on allowed intervals for lateraland longitudinal accelerations.

Definition 43 (Possible Trajectories due to Braking and Normal Driving):Consider, for example, a vehicle c riding on some mad. Given a set ofconstraints, C, on the behavior of the car, then T (C, c) is the set ofpossible future trajectories of c if c complies with the constraintsgiven in C. In some embodiments, the set may be a superset. In someembodiments, T (C_(b), c), T (C_(f), c) may represent the futuretrajectories due to constraints on braking behavior and constraints oncontinue forward behavior.

Definition 43 may be used to refine the notions of safe distance,dangerous situation, blame time, proper response, and responsibility.

Definition 44 (Safe Distance, Dangerous Situation, Blame Time, ProperResponse,

Responsibility): The distance between c₀, c₁ driving on an unstructuredroad is safe if either of the following holds:

-   -   1. For some i∈{0, 1} then T (C_(b), c_(i)∩T(C_(f), c_(1−i))−Ø        and T (C_(b), c_(1−i))∩T (C_(f), c₁)≠Ø    -   2. (C_(b), c₀)∩T (C_(b), c₁)=Ø

In some embodiments, time t is dangerous w.r.t. c₀, c₁ if the distancebetween them is non safe. The corresponding blame time is the earliestnon-dangerous time t_(b) s.t. during the entire time interval (t_(b), t]the situation was dangerous. The proper response of car c_(j) at adangerous time t with corresponding blame time t_(b) is as follows:

-   -   1. If both cars were already at a full stop, then c₁ can drive        away from c_(1−j) (meaning that the absolute value of the angle        between its velocity vector and the vector of the difference        between c_(j) and c_(1−j) should be at most θ, where θ is as in        Definition 42)    -   2. Else, if t_(b) was safe due to item (1) above and j=1−i, then        c_(j) should comply with the constraints of “continue forward”        behavior, as in C_(f), as long as c_(i−j) is not at a full stop,        and after that it should behave as in the case that both cars        are at a full stop.    -   3. Otherwise, the proper response is to brake, namely, to comply        with the constraints

Finally, in case of a collision, the responsibility is on the vehicle(s)that did not respond properly.

In some embodiments, the model may account for the braking constraints,C_(b), and the continue forward behavior constraints, C_(f). Asdescribed above, vehicles can predict what other vehicles will do (othervehicles are supposed to drive on their route, and changelateral/longitudinal speed at a bounded rate), and when a vehicle is ata dangerous time, the proper response may be defined with respect to thegeometry of the route (“brake” laterally and longitudinally). In someembodiments, the proper response is not defined with respect to theother vehicle from which the host vehicle is at a non-safe distance. Forexample, conflicts may arise if a vehicle were at a non-safe distancewith respect to more than a single other vehicle. Therefore, in someembodiments, when designing the definitions for unstructured scenarios,the two properties will still hold.

For example, the constraint definitions may rely on a basic kinematicmodel of vehicles. The vehicle speed may follow the same definition aslongitudinal velocity (bounding the range of allowed accelerations). Forlateral movements, when a vehicle maintains a constant angle of thesteering wheel and a constant speed, it will move (approximately) in acircle. In other words, the heading angle of the car will change at aconstant rate, which is called the yaw rate of the car. Let the speed ofthe car be represented as v(t), the heading angle by h(t). and the yawrate by {dot over (h)}(t) (as it is the derivative of the headingangle). When {dot over (h)}(t) and v(i) are constants, the car moves ona circle whose “radius” is v(t)/{dot over (h)}(t) (where the sign of the“radius” determines clockwise or counter clockwise and the “radius” is ∞if the car moves on a line, i.e. {dot over (h)}(t)=0). Thus, the radiusmay be defined as r(t)=v(t)/{dot over (h)}(t).

In some embodiments, there may be two constraints on driving. The firstis that the inverse of the radius changes at a bounded rate. The secondis that {dot over (h)}(t) is bounded as well. The expected brakingbehavior may be to change {dot over (h)}(t) and 1/r(t) in a boundedmanner during the response time, and from there on continue to drive ona circle (or at least be at a distance of at most ϵ/2 from the circle).This behavior forms the analogue of accelerating by at mosta_(max,accel) ^(lat) during the response time and then deceleratinguntil reaching a lateral velocity of zero.

To make efficient calculations of the safe distance, the superset T(C_(b), c) may be described as follows. Without loss of generality, letthe blame time be t=0, and assume that at the blame time the heading ofc is zero. By the constraint of |{dot over (h)}(t)|≤{dot over (h)}_(max)then |h(ρ)|≤ρ{dot over (h)}_(max). In addition, the inverse of theradius at time ρ must satisfy:

${\frac{1}{r(0)} - {\rho r}_{\max}^{- 1^{\prime}}} \leq \frac{1}{r(\rho)} \leq {\frac{1}{r(0)} + {\rho r}_{\max}^{- 1^{\prime}}}$

where r(0)=v(0)/{dot over (h)}(0). Superset T (C_(b), c) may be definedas all trajectories such that the initial heading (at time 0) is in therange [−ρ{dot over (h)}_(max), −ρ{dot over (h)}_(max)], and thetrajectory is on a circle whose inverse radius is defined as to theabove relationship, and the longitudinal velocity on the circle is as inthe structured case. For the continue forward trajectories, the sameanalysis may apply except that the allowed longitudinal accelerationeven after the response time is in [−a_(max,brake), a_(max,accel)]. Anillustration of the extreme radiuses is given in FIG. 47H.

FIG. 47H is an exemplary illustration of the lateral behavior inunstructured scenes. The black line is the current trajectory. Thedashed lines are the extreme arcs.

Finally, these proper responses of the vehicles may satisfy theaforementioned two properties of the proper response for structuredscenarios: it is possible to bound the future positions of othervehicles in case an emergency will occur; and the same proper responsecan be applied even if the vehicle is in a dangerous situation withrespect to we or more other vehicles.

Pedestrians

The rules for assigning responsibility for collisions involvingpedestrians (or other road users) may follow the same ideas described inprevious subsections. However, it may not be necessary to adjust theparameters in the definitions of safe distance and proper response, orto specify pedestrians' routes (or possibly unstructured routes) ortheir priority with respect to vehicles' routes. In some cases, apedestrian's route is well defined (e.g. a zebra crossing or asidewalk). In other cases, for example, a residential street, the RSSmodel may be based on the analysis for unstructured roads. Additionally,unlike vehicles that are restricted to straight lines or are segments,for pedestrians the change of heading, |{dot over (h)}(t)|, may beconstrained to assume that in an emergency, after the response time, thepedestrian will continue in a straight line. If the pedestrian isstancing, the pedestrian may be assigned all possible lines originatingfrom his current position. The priority may be set according to the typeof the road and, possibly, according to the presence and/or locations oftraffic lights. For example, on a typical residential street, apedestrian may have the priority over the vehicles, and it follows thatvehicles must yield and be cautious with respect to pedestrians. Incontrast, there may be roads with a sidewalk where the vehicles may notneed to assume that a pedestrian on the sidewalk may suddenly run intothe road. In such situations, for example, cars have the priority.Another example is a zebra crossing with a traffic light, where thepriority is set dynamically according to the light. In some embodiments,and as previously described, priority is given not taken, hence even ifpedestrians do not have priority, if the pedestrian entered the road ata safe distance, cars must brake and let them pass.

For example, take a scenario in which a pedestrian that ds on aresidential road. The pedestrian is assigned to all routes obtained byrays originating from its current position. Her safe longitudinaldistance with respect to each of these virtual routes may be short. Forexample, setting a delay of 500 ms, and maximal acceleration and brakingof 2 m/s², yields that the pedestrian's part of the safe longitudinaldistance is 50 cm. It follows that a vehicle may be in a kinematic statesuch that, if it applies a proper response (acceleration for p secondsand then braking) it will remain outside of a radius 50 cm around thepedestrian.

In a second example, a pedestrian nay be standing on the sidewalk infront ° fa zebra crossing. The pedestrian may have a red light, and avehicle approaching the zebra crossing may have a green light. In thisexample, the vehicle route has the priority, hence the vehicle canassume that the pedestrian will stay on the sidewalk. If the pedestrianenters the road while the vehicle is at a safe longitudinal distance(with respect to the vehicle's route), then the vehicle must brake.However, if the pedestrian enters the road while the vehicle is not at asafe longitudinal distance, and as a result the vehicle hits thepedestrian, then the vehicle is not responsible. It follows that in thissituation, the vehicle can drive at a normal speed, without worryingabout the pedestrian.

A third example is when a pedestrian runs on a residential road at 10 kmper hour (which is ≈2.7 m/s). The possible future trajectories of thepedestrian form an isosceles triangle. Using the same parameters as inthe first example, the height of this triangle is roughly 15 m. Itfollows that cars should not enter the pedestrian's route at a distancesmaller than 15 m. But, if the car entered the pedestrian's route at adistance larger than 15 m, and the pedestrian did not stop and, as aresult, crashed into the car, then the responsibility is on thepedestrian.

Cautiousness with Respect to Occlusion

Human sensing capabilities are limited, sometimes because of, forexample, a subconscious decision to focus on a specific part of theroad, sometimes because of carelessness, and sometimes because ofphysical limitations (e.g., it is impossible to see a child hiddenbehind a parked car). While advanced automatic sensing systems may alsosuffer from limited sensing due to physical occlusions or range ofsensor detection. For example, a child may be out of sight behind aparked car, a building or fence may block sight of traffic approachingan intersection, or blind spots may be created by other vehicles on ahighway.

FIG. 471 is an exemplary scenario in which c₀ is trying to exit aparking lot and merge into a route but cannot see whether there are carsapproaching the merge point from the left side of the street. If this isan urban, narrow street, with a speed limit of 30 km/h, a human driver'sbehavior may be to slowly merge onto the road, obtaining more and morefield of view, until sensing limitations are eliminated. Without makingadditional assumptions, this behavior may lead to a collision. Indeed,if c₁ is driving very fast, then at the moment that it enters the viewrange of c₀, C_(i) might reveal that the situation is already dangerousfor more than p seconds and cannot respond properly. Definition 45provides a definition for the first time an occluded object is exposedto the sensor; after its exposure, the system can handle the situationas it would any other object the sensor can detect.

Definition 45 (Exposure Time): The Exposure Time of an object may be thefirst time at which detected by the sensor.

Thus, using Definition 45, it may be possible to set an upper bound onthe reasonable speed of road users. In the previously described example,it is reasonable to assume that c_(i) will not drive Easter than 60 km/h(twice the allowed speed). With this assumption, c₀ can approach themerge point slowly enough so as to make sure that it will not enter adangerous situation with respect to any car whose speed is at most 60km/h. This leads to the following definition.

Definition 46 (Responsibility due to Unreasonable Speed): Consider, forexample, an accident between c₀, c₁ where, before the blame time, therewas a safe lateral distance, and where c₁ was driving unreasonably fast,namely, its average velocity from the exposure time until the blame timewas larger than v_(limit), where v_(limit) is a parameter associatedwith the position of c₁ on the map and on one or more road conditions.In this exemplary situation, die responsibility is solely on c₁.

In some embodiments, application of these definitions allows c₀ to exitthe parking lot safely, in the same manner a human driver does. Based onthe above definition, c₀ may check the situation where there is avehicle at the edge of the occluded area whose velocity is v_(limit).Thus, this encourages c₀ to drive slower and further from the occlusion,thus slowly increasing its field of view and allowing for safe merginginto the street.

This responsibility definition may apply to a variety of cases as it mayspecify what can be occluded (a potentially fast car cannot be occludedbetween two closely parked cars, but a child or pedestrian can). Thisresponsibility definition may also specify what is unreasonably fast foran occluded object or person (a child's v_(limit) is much smaller thanthat of a car).

Occluded Pedestrians in a Residential Area

In one exemplary situation, a child may run out from behind a parkedcar. If the road is in a residential area, the child's route haspriority, and hence a vehicle should adjust its speed such that, if thechild emerges from behind the parked car then there will be no accident.By limiting the maximal speed of the child, the vehicle may adjust speedaccording to the worst-case situation in which the child will be exactlyat the maximal speed.

However, in some embodiments, the above approach may yield a toodefensive behavior. Indeed, consider a typical scenario when a vehicleis driving next to a sequence of parking cars. A child, that runs intothe road (e.g. chasing a ball) at a speed of 10 km/h, might be occludedby a parked car, where the vehicle's camera will sense the child onlywhen the longitudinal distance between the vehicle and the pedestrian issmaller than 0.3 m. Letting the longitudinal safe distance of thechild's route be around 15 m, which is typically more than the width ofthe residential road. Therefore, the vehicle is already at a non-safelongitudinal distance (with respect to the child's route) and must beable to stop before entering the child's route. However, the brakingdistance of a car driving at 1 m/s (with reasonable setting ofparameters) may be more than 0.4 m. It follows that the vehicle shoulddrive slower than 1 m/s in this scenario, even if driving at a lateraldistance of, for example, 5 in, from the parking cars. This may be toodefensive and does not reflect normal human behavior.

In some embodiments, assumptions may be made such that the vehicle doesnot over compensate and drive too defensively. For example, a humandriver may rely on the law. While autonomous vehicles will follow thespeed limit, some embodiments may require more robust notions of safety.Below is an exemplary responsibility definition for this scenario, thatleads to a safer driving while enabling reasonably fast driving.

Definition 47 (Responsibility for Collision with Occluded Pedestrian):Consider, for example, a collision between a pedestrian and a vehicle ata residential road. The vehicle is not responsible for the accident ifthe following two conditions hold:

-   -   Let t_(e) be the exposure time. The vehicle did not accelerate        at the time interval [t_(e), t_(e)+ρ), and performed a        longitudinal brake of at least a_(min,brake) from t_(e)+ρ until        the accident or until arriving to a full stop.    -   The averaged velocity of the vehicle from the exposure time        until the collision time was smaller than the averaged velocity        of the pedestrian at the same time interval (where averaged        velocity is the total distance an agent moved through a time        interval divided by the length of the time interval).

The first condition represents that the velocity of the vehicle may bemonotonically non-increasing from the exposure time until the collisiontime, and the second condition tells us that the averaged velocity ofthe vehicle is smaller than that of the pedestrian. As implied by theproof of the lemma below, under some reasonable assumptions on thepedestrian maximal acceleration, the responsibility definition tells usthat at the collision time, it may be expected that either the velocityof the car will be significantly smaller than that of the pedestrian, orthat both the vehicle and the pedestrian will be at a very slow speed.In the latter case, the damage should not be severe and in the formercase, it complies with “common sense” that the pedestrian is to beblamed for the accident.

The lemma below shows the allowed driving speed that guarantees to neverbe responsible for a collision with an occluded pedestrian.

Lemma 14: Suppose that a vehicle located at a lateral distance of x andlongitudinal distance of y from an occluded spot. Then, if its lateralspeed is zero and its longitudinal speed is smaller than

${v_{\max}\left( {x,y} \right)} = {a_{\min,{brake}}\left( {{- \rho} + \sqrt{\rho^{2} + \frac{x^{2} + y^{2}}{{ya}_{\min,{brake}}}}} \right)}$

it can guarantee to not make an accident of the vehicle'sresponsibility. In particular, a constant driving speed of

${v_{\max}(x)} = {{\min\limits_{y > 0}{v_{\max}\left( {x,y} \right)}} = {a_{\min,{brake}}\left( {{- \rho} + \sqrt{\rho^{2} + \frac{2x}{a_{\min,{brake}}}}} \right)}}$

is possible.

Proof: Suppose that at the exposure time, the pedestrian is located atposition (0, 0) and the car is located at position (x, −y). Suppose thecollision is at the point (x, y_(c)) and let (x, y_(s)) be the point inwhich the car will come to a full stop (if there will be no collision).Define by t_(e) the collision time and by t_(x) the time the vehiclewill reach a full stop. Note that if there is a collision of thevehicle's blame at point (x, y_(t)), then:

$\left. {{x^{2} + y_{c}^{2}} \leq \left( {y_{c} + y} \right)^{2}}\Rightarrow{x^{2} \leq {y^{2} + {2{yy}_{c}}}}\Rightarrow{\frac{x^{2} - y^{2}}{2y} \leq y_{c}} \right.$

But, since y_(s)≥y_(c), this also implies that

$\left. {y_{s} \geq \frac{x^{2} + y^{2}}{2y}}\Rightarrow{{x^{2} + y_{s}^{2}} \leq \left( {y_{s} + y} \right)^{2}} \right.$

which implies that there can be a collision of the vehicle's blame atthe braking time. So, to make sure that there is no collision of thevehicle's blame, verify that there is no such collision at the brakingtime, that is, that the following condition holds:

$y_{s}{\frac{x^{2} - y^{2}}{2y}.}$

Since y_(s)−y+vρ+0.5 v²/a_(min,brake), rearrangement yields:

${\frac{v^{2}}{2a_{\min,{brake}}} + {v\rho} - \frac{x^{2} + y^{2}}{2y}} < 0$

This condition holds for the interval v∈[0, v_(max)(x, y)] wherev_(max)(x, y) is the right root of the quadratic equation, namely:

${v_{\max}\left( {x,y} \right)} = {a_{\min,{brake}}\left( {{- \rho} + \sqrt{\rho^{2} + \frac{x^{2} + y^{2}}{{ya}_{\min,{brake}}}}} \right)}$

Since ƒ(y)=(x₂+y²)/y is minimized at y=x yielding that the maximalconstant speed of the vehicle is:

${v_{\max}(x)} = {a_{\min,{brake}}\left( {{- \rho} + \sqrt{\rho^{2} + \frac{2x}{a_{\min,{brake}}}}} \right)}$

RSS for Advanced Driving Assist Systems

Active safety systems may help make the road safer. For example, anAutonomous Emergency Braking (AEB) system may slow down, or may stop thecar, when it detects that the car is likely to hit the car in front ofit. One problem arising with AEB systems is that they are tuned to haveclose to zero false positives (a false positive is when the systemdetects a car at a dangerous position, while in reality no car is at adangerous position). The price for extremely low false positive rate isa much higher false negative rate (a false negative is when the systemfails to detect a car which is at a dangerous position, and hence thesystem does not respond to the dangerous situation). Thus, there existsa need for constructing a better AEB system relying on a generalizationof the Responsible Sensitive Safety (RSS) concept. In some embodiments,RSS accounts for the tradeoff between false positive 1 false negativebetter than existing systems. The RSS may use a braking profile that cantolerate a higher degree of false positives, and therefore is lessdangerous.

Recall the RSS Safe Distance (Definition 27). RSS's proper response doesnot depend on the underlying driving policy. This definition may beembedded on top of any driving policy. For example, RSS may be embeddedon top of a human driving policy. In this case, whenever a human driverbrings the car to a non-safe distance, the RSS-ADAS system may applybraking so as to bring the car back to a safe distance.

However, applying a strong brake without any warning might be dangerous.Consequently, existing AEB systems are tuned so as to have an extremelylow probability of false positives. The price far extremely low falsepositive rate is a much higher false negative rate (meaning, the systemfails to detect a car which is at a non-safe distance). Thegeneralization of RSS, discussed above, may be used to specify aparticular member of this RSS family that mitigates the danger of falsepositives in an alternative way.

Generalized RSS

In the original definition of RSS, the rear car is assumed to accelerateduring the response time and then to brake until reaching a full stop.This is an example of a braking profile.

More generally:

Definition 48 (Braking profile): A braking profile, B, may be a mappingfrom initial kinematic state of the car (mainly, initial velocity, v₀,and acceleration, a₀) to a pair T_(b), ν, s.t. ν: [0, ∞)

is the future velocity of the car and T_(b)<0 is the first time in whichν(t)=0.

For example, the braking profile applied by the front car in theoriginal definition of RSS may be defined by

$T_{b} = \frac{v_{0}}{a_{\max,{brake}}}$

and ν(t)=max {ν₀−ta_(max, brake), 0}, such that:

${v(t)} = \left\{ \begin{matrix}{v_{0} + {ta}_{\max,{accel}}} & {{{if}\mspace{14mu} t} \leq \rho} \\{v_{0} + {pa}_{\max,{accel}} - {\left( {t - \rho} \right)a_{\min,{brake}}}} & {{{if}\mspace{14mu} t} \in \left( {\rho,T_{b}} \right)} \\0 & {otherwise}\end{matrix} \right.$

Definition 49 (Generalized RSS Safe Distance with respect to BrakingProfiles: B_(f); B_(r)) A longitudinal distance between a car c_(r) thatdrives behind another car c_(f), where both cars are driving at the samedirection, is safe with respect to braking profiles B_(r); B_(r) if incase the front car applies braking profile B_(f) and the rear carapplies braking profile B_(r), then the cars will reach a full stopwithout colliding.

The proper response may be defined as follows:

Definition 50 (Proper response): Suppose the first time that thedistance between cc and c_(r) is non-safe is t₀, and without loss ofgenerality set t₀=0. Then, the proper response for the front car is tohave its velocity at least v_(f)(t), where v_(f) is the velocity definedby B_(f), and the proper response for the rear car is to have itsvelocity at most v_(r)(t), where y_(r) is the velocity defined by Br.

If both cars apply proper response then there will be no accident.

Jerk-Bounded Braking Profile

The jerk-and-acceleration-bounded braking profile may be denoted Bj. Thevehicle may start decreasing acceleration linearly (with slope j_(max)),until reaching a max brake parameter (denoted a_(min,brake)), and thencontinue to brake with a constant deceleration until reaching zerovelocity. The following closed form formulas for may be used forcalculating this braking profile.

Braking with a Constant Jerk: Suppose the vehicle starts braking at jerkof j_(max). Suppose also that the vehicle can come to acceleration 0immediately, so below, assume a₀≤0. Then, the dynamics of the car is asfollows:

a(t)=a ₀ −j _(max) ^(t)

v(t)=v ₀+∫_(τ=0) ^(t) a(τ)dτ=v ₀+[a ₀τ−½j _(max)τ²]₀ ^(t) =v ₀ +a ₀ t−½j_(max) t ²

x(t)=x ₀+∫_(τ=0) ^(t) v(τ)dτ=x ₀+[v ₀τ+½a ₀τ²−⅙j _(max)τ³]₀ ^(t) =x ₀ +v₀ t+½a ₀τ²−⅙j _(max) t ³

Braking profile: Based on these equations, braking distance will bedefined as follows. Let T be the first time in which either a(T)a_(min,brake) or νT)=0, that is, t=min{T₁, T₂} where

${T_{1} = \frac{a_{0} + a_{\min,{brake}}}{j_{\max}}},{T_{2} = \frac{a_{0} + \sqrt{a_{0}^{2} + {2j_{\max}v_{0}}}}{j_{\max}}}$

The time for reaching fill brake is

$T_{b} = \left\{ \begin{matrix}T_{2} & {{{if}\mspace{14mu} T} = T^{2}} \\\frac{v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}}{a_{\min,{brake}}} & {otherwise}\end{matrix} \right.$

And the speed is as follows

${v(t)} = \left\{ \begin{matrix}{v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}} & {{{if}\mspace{14mu} t} \leq T} \\{v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}} - {\left( {t - T} \right)a_{\min,{brake}}}} & {{{if}\mspace{14mu} t} \in \left( {T,T_{b}} \right)} \\0 & {otherwise}\end{matrix} \right.$

Braking distance: Finally, the car will move the following distanceuntil reaching a full stop:

$\left\lbrack {{v_{0}T} + {\frac{1}{2}a_{0}T^{2}} - {\frac{1}{6}j_{\max}T^{3}}} \right\rbrack + \frac{\left( {v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}} \right)^{2}}{2a_{\min,{brake}}}$

Safe distance with respect to Bf and Bj

Suppose that the front car brakes with braking profile B_(f) (brakingwith a constant deceleration of a_(max,brake)), and the rear car relieson braking profile B_(j). Then, the safe distance formula is

$\left\lbrack {\left\lbrack {{v_{0}T} + {\frac{1}{2}a_{0}T^{2}} - {\frac{1}{6}j_{\max}T^{3}}} \right\rbrack + \frac{\left( {v_{0} + {a_{0}T} - {\frac{1}{2}j_{\max}T^{2}}} \right)^{2}}{\left. 2 \middle| a_{\min,{brake}} \right|} - \frac{v_{f}^{2}}{\left. 2 \middle| a_{\min,{brake}} \right|}} \right\rbrack_{+}$

The ADAS RSS System

As soon as the distance becomes non-safe (according to the jerk-basedformula), the system may alert the driver and may start to brake with ajerk of j_(max) until one of the following happens: (1) the car stops(2) the distance becomes non-safe (3) the driver turns off the RSSsystem (by a button or some other mechanism).

The same proof of RSS may be adjusted to show that if the driver did notturn-off the system, then there can be no accident of the ego vehicle'sresponsibility. As an example, if all vehicles follow the RSS rules thenthere will be no accidents at all (clue to driving policy errors,sensing mistakes or malfunctioning can still happen). Therefore, if aregulatory body adopt the ADAS RSS system it may reduce the caraccidents significantly.

A Better Handling of False Positives

The same hardware that implements AEB may be adjusted to implement ADASRSS. Because the braking profile is jerk bounded, the danger of falsepositives is not very severe (the driver is not surprised, and someonebehinds the rear car will also not be surprised because of the bound onthe jerk). Therefore, it is possible to tune the system to have lessfalse negatives.

Navigation with a Safe Longitudinal Distance

As described above. RSS may be effective for determining a safe distancebetween host vehicle and another object (e.g., one or more targetvehicles or VRUs). RSS provides a set of mathematical formulae that canbe used to ensure that a vehicle implementing RSS will not be involvedin an accident caused by it. As discussed above, RSS may be applied tomaintain a safe distance between two vehicles traveling in the samedirection. In other embodiments, however, RSS may also be used tomaintain a safe distance between two vehicles traveling in oppositedirections. For example, two vehicles may be driving towards each otherduring a lane change or while navigating a parking lot. In someinstances, a vehicle may be traveling on the wrong side of the road. RSSmay be used to ensure that a host vehicle maintains a safe distanceaccounting for both vehicles and braking (and/or steering) if neededsuch that the vehicles come to a complete stop (or otherwise avoid oneanother) without causing a collision.

FIG. 48A illustrates an example scenario with two vehicles traveling inopposite directions consistent with the disclosed embodiments. In thisscenario, a host vehicle 4802 may be traveling along a lane of atwo-lane road, as shown in FIG. 48A. A target vehicle 4804 may betraveling in the opposite direction of host vehicle 4802 in a laneoccupied by host vehicle 4802. For example, target vehicle 4804 may bepassing a second oncoming vehicle 4806 and may enter the lane of travelof host vehicle 4802 in order to complete the passing maneuver. Thus,host vehicle 4802 and target vehicle 4804 may be traveling toward eachother in opposite directions. Various other scenarios may exist wheretwo vehicles are traveling in opposite directions. For example, hostvehicle 4802 may be performing the passing maneuver and may enter thelane of travel of target vehicle 4804. The two vehicles may be travelingtowards each other in other situations, such as in a parking lot, whenthey are both proceeding through an intersection, or any other similarscenario. The present disclosure is not limited to any particularscenario in which a direction of travel of a target vehicle is towardthe host vehicle.

Host vehicle 4802 may be configured to perform a planned navigationalaction if it allows host vehicle 4802 to maintain a safe longitudinaldistance from vehicle 4804, such as an RSS safe distance, as discussedabove. In the scenario shown in FIG. 48A, for example, the plannednavigational action may be to maintain a forward heading direction or tomaintain a throttle action of host vehicle 4802. In other embodiments,the planned navigation action may be one that would cause host vehicle4802 and target vehicle 4804 to travel towards each other in oppositedirections. For example, the navigational action may include a passingmaneuver, in which host vehicle 4802 attempts to pass another vehicleand enters a lane occupied by target vehicle 4804. Host vehicle 4802 maybe configured to perform the passing maneuver if a safe distance wouldbe maintained between host vehicle 4802 and target vehicle 4804. Thenavigation action may include other maneuvers as well, such as a lanechange maneuver, a merge maneuver, a parking lot navigation maneuver(e.g., entering a parking spot, leaving a parking spot, parallelparking, maneuvering between parking rows, etc), an intersectionmaneuver (e.g., turning across oncoming traffic, proceeding through ayellow light, etc), or the like.

In the example scenario of FIG. 48A, the direction of target vehicle4804 is toward host vehicle 4802 in a fully “head-on” situation. Thepresent disclosure may equally apply to situations in which thedirection of target vehicle 4804 is toward host vehicle 4802 at anangle. Accordingly, the term “toward” as used herein should include anysituation in which a substantial component of the target vehicle'straveling direction is in the direction of the host vehicle. The term“toward” may also refer to a situation in which the frontal corridor oftwo or more vehicles at least partially overlap.

FIG. 48R illustrates an example scenario of a target vehicle 4804traveling towards a host vehicle 4802 consistent with the disclosedembodiments. Host vehicle 4802 may be traveling in a direction 4812 andtarget vehicle 4804 may be traveling in a direction 4814 that intersectsdirection 4812. Directions 4812 and 4814 may intersect at an angle, Θ,as shown. In a “head on” situation, where host vehicle 4802 and 4804 aretraveling directly at each other, angle Θ may be equal or substantiallyequal to zero. Target vehicle 4804 may be considered to travel towardhost vehicle 4804 at other angles as well. For example, in someembodiments, direction 4814 of target vehicle 4804 may be considered tobe toward host vehicle 4802 as long as angle Θ is less than 90 degrees.In other embodiments, angle Θ may be required to be less than anotherangle (e.g., 60 degrees, 45 degrees, 30 degrees, etc.). Direction 4814may also be defined based on longitudinal and lateral components (x andy, respectively) in relation to host vehicle 4802. Direction 4814 ofvehicle 4804 may be considered to be toward host vehicle 4802 as long asx is some nonzero component of direction 4814 in the direction of hostvehicle 4802. In some embodiments, a relationship between component xand component y may also be defined. For example, direction 4814 oftarget vehicle 4804 may be considered to be toward host vehicle 4802 aslong as component x is greater than component y (representing an angle Θof 45 degrees). Accordingly, it is to be understood that thelongitudinal safety distance is not limited to direct “head on”situations and may be at various other angles.

As discussed above, the RSS safe distance may correspond to a distancebetween a host vehicle and a target vehicle at which the host vehiclemay come to a stop without colliding with the target, assuming certainconditions. The RSS safe distance may include a calculation of theminimum distance that it would take the vehicles to stop if braking atpredetermined braking rates and after an assumed behavior duringcorresponding reaction times for the vehicles. For example, the RSS safedistance accounts for the possibility that the two cars travel towardone another both with a maximum acceleration during a reaction timebefore each braking at a predetermined braking level to come to acomplete stop. Taking into account the vehicles' maximum accelerationduring reaction times allows navigation according to the RSS distance toensure no collisions occur even in worst case scenarios,

FIG. 49 illustrates an example of host vehicle maintaining a safelongitudinal distance consistent with the disclosed embodiments. Targetvehicle 4904 may be traveling in a direction toward host vehicle 4902. Aprocessing device of host vehicle 4902 (e.g., processing unit 110) maydetermine a planned navigational action for accomplishing a navigationalgoal of the host vehicle. Host vehicle 4902 may be configured to performthe planned navigational action if an RSS safe longitudinal distance canbe maintained between host vehicle 4902 and target vehicle 4904. Asdiscussed above, the planned navigational action may include variousmaneuvers, such as a lane change maneuver, a merge maneuver, a passingmaneuver, a maintain forward heading maneuver, a parking lot navigationmaneuver, or a maintain throttle action, or other similar navigationalactions. The processing device of host vehicle 4902 may determine anext-state distance 4910 between host vehicle 4902 and target vehicle4904 corresponding to a distance between the vehicles that would resultif the planned navigational action was taken. The processing device mayalso determine a stopping distance 4912 in which vehicle 4902 can bestopped and a stopping distance 4914 in which vehicle 4904 can bestopped. The processing device of host vehicle 4902 may implement theplanned navigational action if the determined next-state distance 4910is greater than a sum of stopping distance 4912 and stopping distance4914, thereby indicating the vehicles can both come to a complete stopto avoid a collision.

The stopping distances 4912 and 4914 may be calculated in any mannerdescribed above in relation to RSS. For example, the distance needed tocome to a stop may be calculated using a vehicle braking rate, a vehiclemaximum acceleration capability, and a current speed of the vehicle. Insome embodiments, the current speed of the host vehicle may bedetermined based on an output of one or more sensors. For example, thecurrent speed may be determined from an output of an accelerator, aLIDAR system, a RADAR system, a GPS unit, or the like. As anotherexample, the current speed of the host vehicle may be determined byanalyzing one or more images (e.g., based on a scaling rate change of afixed object detected in two or more images).

In some embodiments, the disclosed embodiments may assume that a vehiclewill brake at its maximal braking capability to avoid a collision. Forexample, the braking rate may be based on based on at least onerecognized characteristic of the vehicle. For host vehicle 4902, themaximal braking rate may be known or estimated by the system based oncharacteristics of the car, previous braking maneuvers, or the like. Fora target vehicle, the maximal braking capability may be determined basedon at least one characteristic of the target vehicle. The at least onecharacteristic may be any characteristic that is known to correlate witha braking capability or that may correlate with a braking capability. Insome embodiments, the recognized characteristic of the target vehiclemay include a vehicle type, which may be determined based on analysis ofimages containing representations of the target vehicle. The vehicletype may be, for example, a general category to which the target vehiclebelongs (e.g., full-size sedan, compact car, SUV, cross-over SUV,motorcycle, etc.) or a more particular category or sub-categoryassociated with the target vehicle. In some embodiments, the recognizedcharacteristic of the target vehicle may include a vehicle model, brandname, or other classifier of the target vehicle (e.g., Toyota Prius®,BMW X5®, etc.). The processing device may be programmed to assume thatthe target vehicle has a maximum braking capability corresponding withthat of a known braking capability of that vehicle type or a class ofvehicles. The processing device may use the vehicle type to, forexample, access a database containing known braking capabilities or eachvehicle type. For example, if the detected vehicle type is BMW X5®, theprocessing device may look up the reported braking capabilities of a BMWX5® from a database. If there are multiple maximum braking capabilitiesreported for a vehicle model (for example, a BMW X5® may have differentbraking capabilities depending on whether it has the xDrive40i orxDrive50i trim level or depending on the year of its manufacture), theprocessing device may be programmed to assume the target vehicle has thebest maximum braking capability reported for that vehicle model. Therecognized characteristic or the target vehicle may also include anindicator of whether the target vehicle is an autonomous vehicle,partially autonomous vehicle, or whether the target vehicle ishuman-operated. Such information may be derived from analysis ofcaptured images (e.g., images acquired from one or more cameras onboardthe host vehicle) or may be broadcast from the target vehicle viawireless communication.

In some embodiments, the recognized characteristic of the target vehiclemay include a vehicle size. The vehicle size may be a relative size, apredetermined size, or the like. The vehicle size may correspond to aphysical size of the vehicle and/or an estimated weight of the vehicle.For example, the processing device may determine that the target vehicleis larger or smaller than the host vehicle. In another example, theprocessing device may be programmed to classify the target vehicle intoone or a plurality of predetermined vehicle sizes, each of which mayinclude a range of sizes (e.g., category 1=less than 1,000 kg; category2=1,000-1500 kg; category 3=1,500-1,800 kg; and so forth). Some vehiclesmay contain an indication of its size, which may be used to determine avehicle size of the target vehicle. For example, the target vehicle maybe a GMC Sierra® and may include an indication or model name on theexterior of the vehicle associated with its size, such as 1500, 2500,2500 HD, and so forth.

Applying maximal braking, especially when such application is sudden,may be regarded as an extreme response that should be reserved for caseswhen it is not avoidable, tinder certain circumstances, maximal brakingcan be uncomfortable to passengers, can implicate trailing vehicles, canexcessively wear down vehicle hardware (tires, brace pads etc.), etc.Accordingly, the stopping distance for the vehicle may assume apredetermined submaximal braking rate that is less than a maximumbraking rate capability of the host vehicle. For example, the submaximalbraking rate may assume a gradual application of the brake from aninitial braking force (that is less than the maximum braking capabilityof the vehicle) to the maximum braking capability of the vehicle ratherthan an immediate application of the maximum braking capability. In someembodiments, the submaximal braking rate may be an ideal orstatistically acceptable braking rate. For example, data relating to thebraking rate at which most humans come to a stop may be used todetermine: submaximal braking rate. In some embodiments, the submaximalbraking rate may be set according to a user preference. For example, afirst passenger may provide a first the submaximal braking rate that iscomfortable to him or her, a second passenger may provide a second thesubmaximal braking rate that is comfortable to him or her, and so forth.In some embodiments, a processing device may determine the submaximalbraking rate based on, for example, one or more sensed road conditions(e.g., dirt road, road traction properties, etc.), traffic conditions(congestion level, average distance between, vehicle around the hostvehicle, rate of cut-ins in front of the host vehicle, etc.), one ormore vehicle characteristics, one or more sensed weather conditions, orthe like. For example, a processing device may determine a submaximalbraking rate that provides the maximum safety and comfort on a snowyroad, a submaximal braking rate that provides the maximum safely andcomfort on a dry highway, and so forth. It will be appreciated, thatwhile implementing the submaximal braking rate can help increase comfortand have other positive impacts on the behavior of the host vehicle, itcan also have less desirable effects, in particular, if the submaximalbraking rate is small, so that braking may become “relaxed” or not asstrong. For example, using a small submaximal braking rate may have astrong negative effect on efficiency, by causing the vehicle to alwayskeep an exaggerated distance from the vehicle ahead. This may cause anannoyance to other road users and prevent the host vehicle fromeffectively negotiating complex scenarios such as merging and driving incongested areas. Thus, in some examples, a submaximal braking rate thatbalances performance or efficiency with comfort (while maintaining RSSsafety) may be set, selected or determined.

Consistent with this disclosure, the submaximal braking rate may be aconstant. For example, the submaximal braking rate may be a braking ratethat corresponds with a deceleration of 2 m/s², 10 m/s², or any otherconstant deceleration. In some embodiments, the submaximal braking ratemay be a constant that is proportional to the maximum braking ratecapability of a host vehicle. For example, the submaximal braking ratemay be 20%, 33%, 50%, 70%, or any other percentage of the maximumbraking capability of the host vehicle. In some embodiments, thesubmaximal braking rate may be a linear function of the current speed ofthe host vehicle, such that the brake is gradually applied from theminimum braking capability of the host vehicle up Lo, at most, themaximum braking capability of the host vehicle. For example, asubmaximal braking rate may be determined that allows the host vehicleto come to a stop from its current speed without reaching the maximumbraking capability of the vehicle. As another example, a submaximalbraking rate may be determined that eventually reaches the maximumbraking capability of the host vehicle such that the host vehicle brakesat less than maximum braking capability for a first portion of astopping maneuver and brakes at its maximum braking capability for asecond portion the stopping maneuver. In some embodiments, thesubmaximal braking rate may be a different function of the current speedof the vehicle. For example, the submaximal braking rate may be abraking rate that is exponentially or logarithmically applied until thevehicle comes to a stop.

In some embodiments the submaximal braking rate may be determined basedon a blame or responsibility determination associated with host vehicle4902 or target vehicle 4904. From a responsibility perspective, hostvehicle 4902 may have an obligation to brake, but at a lower rate thantarget vehicle 4904. For example, target vehicle 4904 may be travelingin an incorrect direction for a given lane or roadway, as shown in FIG.48A, and thus may have a greater obligation to brake. Accordingly, thehost vehicle braking rate may be less than the target vehicle braking,rate, or vice versa.

As discussed above, an RSS distance may include be dependent upon themaximum possible acceleration capability that the vehicle may experienceduring a period between a sensed event and a vehicle's reaction to asensed event (i.e., a reaction time associated with the host vehicle).Accordingly, the stopping distance may also include a vehicleacceleration distance that corresponds to a distance the vehicle cantravel during a vehicle reaction time at the vehicle's maximumacceleration capability, starting from the determined current speed ofthe vehicle. For example, the disclosed embodiments may account for adelay between the period in which host vehicle 4902 or target vehicle4904 begins applying the brake or making another navigational maneuver.For example, there may be several milliseconds (or more or less) betweenthe time host vehicle 4902 detects that target vehicle 4904 is travelingtowards host vehicle 4902. The processing device may account for theacceleration that may occur during response period ρ, corresponding tothe vehicle's reaction time. Response period p may correspond to a knowncharacteristic of a vehicle, similar to the braking rate, or may be anassumed value for all cars (e.g., a certain reaction time forhuman-operated vehicles and another value (possibly different) forautonomous vehicles). For example, let v₁ be the current velocity of thevehicle. The stopping distance for a vehicle may include a first termcorresponding to a distance the vehicle travels as a result of a maximumacceleration during the reaction time. The stopping distance may alsoinclude a distance the vehicle requires to reduce its velocity to 0, ata predetermined braking rate (e.g., a maximal braking rate or asubmaximal braking rate), from its final velocity at the end of thereaction time period.

As noted, the velocity of the vehicle used in the RSS and/or stoppingdistance determination may correspond to a maximum velocity of the hostvehicle after accelerating for its response period, ρ (e.g., at itsmaximum acceleration capability). For example, let v₁ be a currentvelocity of the vehicle, let ρ be the response period, and leta_(max,accel) be the maximum acceleration of the vehicle, then themaximum velocity v_(max,ρ) of the vehicle after the response period ρis:

v _(max,ρ) =v _(⊥) +ρa _(max,accel)

Accordingly, v_(max,ρ) may be used in determining the stopping distanceof host vehicle 4902 and/or target vehicle 4904. For example, theprocessing device may assume the maximal or submaximal braking rate isapplied starting at a speed of v_(max,ρ) in determining the stoppingdistance of the vehicle.

In some embodiments, the processing device of host vehicle 4902 may beconfigured to implement the planned navigational action if thedetermined next-state distance is greater, by at least a predeterminedminimum distance (e.g., 0 or any suitable distance greater than 0, suchas 0.5 m, 1 m, 2 m, etc.), than the sum of the stopping distance 4912for host vehicle 4902 and the stopping distance 4914 of target vehicle4904. If the RSS safe longitudinal distance includes a non-zero minimumapproach distance component, then in the safe distance determination,host vehicle 4902 would come to a stop at least the minimum distancefrom the target vehicle. The minimum distance may be predetermined(e.g., a minimum distance of 0.5 m, 1 m, 2 m, etc.). The minimumapproach distance may be determined based on any set of factorsconsistent with this disclosure. In some cases, the minimum approachdistance may be based on vehicle velocity. For example, a minimumapproach distance may be set higher for higher rates of sensed velocityrelative to either host vehicle 4902 or target vehicle 4904. The minimumapproach distance may also depend on a sensed weather condition (e.g.,where snow or water is sensed on a road, or where a sensed tractionindicator suggests less than optimal traction, the minimum approachdistance may be increased to provide an additional safety buffer. Theminimum approach distance may also be set based on a user's preferences,etc.

FIGS. 50A and 50B provide flowcharts depicting an exemplary process 5000for maintaining a safe longitudinal distance consistent with thedisclosed embodiments. Process 5000 may be perforated by at least oneprocessing device, such as processing unit 110, described above. Process5000 is exemplary, and one of ordinary skill in the art having thebenefit of this disclosure may understand that process 5000 may includeadditional steps, exclude certain steps, or may be otherwise modified ina manner consistent with this disclosure,

Process 5000 may include a step 5002 for receiving at least one imagerepresentative of an environment of the host vehicle. The at least oneimage may be received from an image capture device, which may be anyimage capture device consistent with this disclosure, including imagecapture device 122. In some embodiments, the at least one image may bean image obtained from any of a camera, a RADAR, a LIDAR, or any otherdevice from which an image may be obtained, whether optical orotherwise. There may some period of delay between the time when theimage is captured and time when the processing device receives theimage. Further, there may a period of delay between the time when anevent occurs and the imaging device captures an image of the event. Forexample, if a target vehicle enters a lane in front of a host vehicle,there may be a short period (e.g., a millisecond, 2 milliseconds, 5milliseconds, etc.) between when the target vehicle maneuvers into thelane and when the imaging device captures (an processes) an image of thetarget vehicle.

Process 5000 may include a step 5004 for determining a plannednavigational action for the host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed todetermine a planned navigation action for accomplishing a navigationalgoal of the host vehicle. The navigation action may be determined basedon at least one driving policy. The planned navigation action and/or theat least one driving policy may be any consistent with this disclosure,including those discussed above. For example, the planned navigationaction may include at least one of a lane change maneuver, a mergemaneuver, a passing maneuver, a maintain a forward heading maneuver, aparking lot navigation maneuver, or a maintain throttle action.

Process 5000 may include a step 5006 for analyzing the at least oneimage to identify a target vehicle in the environment of the hostvehicle. The at least one image may be an image received from an imagecapture device, such as image capture device 122. The at least one imagemay be the one or more images received as part of step 5002 of process5000.

Process 5000 may include a step 5008 for determining a next-statedistance associated with the planned navigation action. Consistent withthis disclosure, the processing device may be programmed to determine anext-state distance between the host vehicle and the target vehicle thatwould result if the planned navigation action was taken. The next-statedistance may be calculated by any means disclosed herein, including theRSS safe distance described above. For example, if the plannednavigation action is an acceleration of the host vehicle, the next-statedistance may be an expected distance between the host vehicle andleading target vehicle in front of the host vehicle after thenavigational action is taken.

Process 5000 may include a step 5010 for determining a host vehiclebraking rate, a host vehicle maximum acceleration capability, and acurrent speed of the host vehicle. Each of the factors, (i.e., thevehicle braking rate, the maximum acceleration capability, and the speedof the host vehicle) may be determined by any means consistent with thisdisclosure. The vehicle braking rate may represent a maximal brakingrate associated with the vehicle, or may be a submaximal braking rate,as described above. In some embodiments, the vehicle braking rate and/orthe maximum acceleration capability of the host vehicle may bedetermined based on, for example, the current speed or the vehicle, roadconditions (e.g., a slope of the road, a material of the road, etc.),weather conditions (e.g., snowy, humid, etc.), vehicle conditions (e.g.,tire pressure, brake-pad condition, current load of the vehicle, etc.),or the like. In some embodiments, one or more of the factors may bedetermined based on an output of one or more sensors. For example, ahost vehicle may contain an accelerometer, which may provide an outputto the processing device, and that output may include a current speed ofthe host vehicle and/or an acceleration capacity of the host vehicle. Insome embodiments, the processing device may determine a current speed ofthe host vehicle and use the current speed to determine a currentvehicle braking rate and/or a current acceleration capability. Forexample, the vehicle braking rate of a vehicle traveling at a firstspeed (e.g., 15 km/hr) may be significantly different from the vehiclebraking rate of the same vehicle traveling at a second speed (e.g., 30km/hr). In some embodiments, one or more of the vehicle braking rate,the maximum acceleration capability, and/or the speed of the hostvehicle may be assumed using a predetermined value. For example, theprocessing device may be configured to assume that the host vehicle hasa maximum braking capability corresponding with a predetermined valuecorresponding with an average (or the worst) maximum braking capabilityof the type of vehicle associated with the host vehicle. In someembodiments, each factor may be determined based on external conditionsof the road or temporary characteristics of the vehicle. For example,the vehicle braking rate of the host vehicle may be determined based ona sensed condition of a road surface. In this example, the sensed roadcondition may include a roughness of the road, a slant or slope of theroad, the present or absence of a substance or object on the road,whether the road is asphalt, cement, gravel, or another material, or anyother condition consistent with this disclosure. As another example, thevehicle braking rate of the host vehicle may be determined based on asensed weather condition. In this example, the weather condition mayinclude a detection of any precipitation (e.g., rain, sleet, snow, ice,etc.), a weather condition that affects visibility (e.g., fog, smog,smoke, etc.), a weather condition that may affect the handling of thevehicle (e.g., strong winds, high heat, etc.), or any other weathercondition that may affect a navigational response of the host vehicle.In another example, processing device may determine a vehicle brakingrate based on whether the host vehicle contains, for example, onepassenger or a plurality of passengers, cargo of a significant weight, atrailer, etc. Such conditions may be sensed based on analysis of imagesacquired by onboard cameras (e.g., recognizing snow or water on aroadway, water on a windshield, road surface smoothness, etc.) or may bebased on any other suitable sensors. Such sensors may include wheel slipsensors, braking system sensor outputs, receivers of signals transmittedfrom roadside infrastructure, weather data streamed via a Wi Ficonnection, GPS and/or speedometer outputs, etc.

In some embodiments, the vehicle braking rate and/or the maximumacceleration capability may be determined based on one or morepredefined factors. For example, a government or industry entity mayprovide one or more regulations that dictate a vehicle braking rateand/or a maximum acceleration capability that a vehicle or class ofvehicles may have and the at least one processor may assume that thatthe host vehicle has the vehicle braking rate and/or the maximumacceleration capability allowed by the regulations. Constraints on themaximum braking and/or maximum acceleration values may also beuser-defined (e.g., an occupant of an autonomous vehicle may select oneor more vehicle setting that correspond to predetermined maximumallowable braking and acceleration levels), scenario-defined (e.g.,based on circumstances at a particular location and/or during aparticular navigation scenario), and/or based on observed performance(e.g., based on historical data collected during autonomous navigationand/or navigation by a user).

Process 5000 may include a step 5012 for determining a stopping distancefor the host vehicle. Consistent with this disclosure, the processingdevice may be configured to determine a stopping distance for the hostvehicle based on the host vehicle braking rate, the host vehicle maximumacceleration capability, and/or the current speed of the host vehicle(e.g., as described in detail above). The stopping distance for the hostvehicle may be determined by any means consistent with this disclosure.For example, the processing device may use one or more of the formulasdiscussed in relation with RSS above.

In some embodiments, a stopping distance may be a distance that a hostvehicle needs to come to a stop, given its current speed, if the hostvehicle were to accelerate at its maximum acceleration capability forperiod of time before braking at a predetermined braking capability. Forexample, the stopping distance for the host vehicle may include anacceleration distance that corresponds to a distance the host vehiclecan travel over a predetermined time period at the current maximumacceleration capability of the host vehicle, starting from thedetermined current speed of the host vehicle. The predetermined timeperiod may be a time period assumed by the processing device. Forexample, a constraint may dictate that the processing device assumes ahost vehicle will accelerate for a certain time period (e.g., 0.5milliseconds, 1 millisecond, 2 milliseconds, 3 milliseconds, 10milliseconds, etc.). The predetermined time period may be a reactiontime associated with the host vehicle. For example, the predeterminedtime period may be a delay between the time when a sensor (e.g., animaging device) of the host vehicle captures an image of a conditionthat requires a braking response from the host vehicle (e.g., a targetvehicle coming into the path of the host vehicle) and the time when thehost vehicle begins braking at its vehicle braking rate. Such timeperiods may include processing times associated with analysis of thecaptured image, planning a navigational response based on one or moreprocessor-implemented driving policies, and implementing thenavigational response through control of one or more actuatorsassociated with a steering and/or braking system (among others) of avehicle. In this example, it may be assumed that, in a worst-casescenario, the host vehicle accelerates at its maximum accelerationcapability for the entirety of the delay period. In some embodiments,the time period associated with the reaction time may be determined orapproximated by the processing device. For example, the processingdevice may monitor the time between receiving an image and determiningthat a braking response is needed. As another example, the processingdevice may determine a mean, median, or mode reaction time associatedwith a plurality of navigational responses and use the mean, median, ormode reaction time when calculating a stopping distance. For example,after tens, hundreds, or thousands of navigational responses, theprocessing device may determine that the average time between a sensedevent and a navigational response is a particular value (e.g., any realnumber of milliseconds) and use that value as the reaction timeassociated with the host vehicle. In some cases, the reaction time usedin the RSS distance determination may be vehicle-specific and mayinclude a running average of a measured reaction time for the particularvehicle to various sensed conditions.

Consistent with this disclosure, a determined stopping distance mayinclude a minimum distance between the host vehicle and the targetvehicle after coming to a complete stop. The determined or predeterminedminimum distance may correspond with a predetermined separation distanceto be maintained between the host vehicle and other vehicles. Forexample, the processing device may be programmed to include a determinedor predetermined minimum distance in a calculation of a stoppingdistance. For example, a predetermined separation distance may be atleast one meter. In this example, the determined or predeterminedminimum distance may be d_(min) as discussed above.

Process 5000 may include a step 5014 for determining a current speed ofthe target vehicle, a target vehicle maximum acceleration capability,and a target vehicle braking rate. Consistent with this disclosure, theat least one processing device may be programmed to determine a currentspeed of a target vehicle. In some embodiments, the speed of the targetvehicle may be determined based on the speed of the host vehicle. Forexample, one or more sensors on a host vehicle may provide informationrelated to the speed of the host vehicle and an indication of theacceleration or change in direction of a target vehicle in relation tothe host vehicle. In some embodiments, the target vehicle speed may bedetermined based on analysis of at least one image. The at least oneimage may be, for example, the same image received by the processingdevice at step 5002 that was used to identify the target vehicle at step5006. In some embodiments, a plurality of images may be analyzed todetermine a speed of the target vehicle. For example, a first image maydepict the target vehicle a first distance from the host vehicle and asecond image may depict the target vehicle a second distance from thehost vehicle, the processing device may use the change in distance andthe time between the first and second images to determine a speedassociated with the target vehicle. In some embodiments, the targetvehicle speed may be determined based on analysis of an output from atleast one of a LIDAR system or a RADAR system associated with the hostvehicle. For example, the processing device may use the speed of thehost vehicle and a distance between the host vehicle and the targetvehicle (as sensed by, for example, a LIDAR system) to determine a speedof the host vehicle.

In some embodiments, to account for a worst-case scenario, theprocessing device may be programmed to assume that the current speed ofthe target vehicle is less than or more than a sensed speed of thetarget vehicle. For example, if the target vehicle is traveling in frontof the host vehicle, the processing device may be programmed to reduce asensed speed using a predetermined value, a percentage, a formula, orthe like. Its the processing device determined, based on informationfrom one or more sensors, that a target vehicle is traveling at 100km/hr, it may adjust the sensed speed by 10% to assume that the vehicleis traveling at 90 km/hr. The speed or a target vehicle may becorrelated with t braking rate of the target vehicle so assuming areduced speed of the target vehicle is akin to assuming the targetvehicle may stop quicker than it otherwise might (e.g., a target vehiclemay stop in a shorter distance if traveling at 90 km/hr than iftraveling at 100 km/hr).

Consistent with this disclosure, the at least one processing device maybe programmed to assume a maximum acceleration capability and/or vehiclebraking rate of the target vehicle based on at least one recognizedcharacteristic of the target vehicle. The at least one characteristicmay be any characteristic that is known to correlate with anacceleration or braking capability or that may correlate with anacceleration or braking capability. In some embodiments, the recognizedcharacteristic of the target vehicle may include a vehicle type, class,make, model, size, or the like, as described above.

The processing device may be programmed to recognize the at least onecharacteristic from information from one or more sensors (e.g., LIDAR,RADAR, imaging devices, etc.). In some embodiments, the recognizedcharacteristic of the target vehicle may be determined based on analysisof the at least one image. For example, the image of the target vehiclemay include a text on the exterior of the target vehicle, which may beused to determine a vehicle type, vehicle model, vehicle size, or othercharacteristic. As another example, the image of the target vehicle mayinclude other objects that may be used to approximate a vehicle size orother characteristic based on comparison with the other objects. As anexample, a large vehicle may appear taller than a speed-limit signwhereas a small vehicle may appear shorter than a speed-limit sign. Insome embodiments, the at least one characteristic of the target vehiclemay be determined based on at least one of a LIDAR output or a RADARoutput. For example, a LIDAR output may include a first distanceassociated with the distance to the rear bumper of the target vehicleand a second distance associated with a distance to the front bumper (orother area) of the target vehicle, the difference between which may beused to estimate the size of the target vehicle. Sizes of targetvehicles may also be estimated based on known sizes of imaged features(e.g., brake lights, tires, side view mirrors, etc.). A determination ofhow an object scales from one image to another may also be used topredict a target vehicle size or range.

As discussed above, the target vehicle braking rate may correspond to amaximal or submaximal braking rate of the vehicle. The target vehiclebraking rate or target vehicle maximum acceleration capability may bedetermined by any means consistent with this disclosure, including themeans described above in step 5010 for the host vehicle. For example,the target vehicle braking rate may be determined based on a sensedcondition of a road surface, a sensed weather condition, etc. In someembodiments, the vehicle braking rate may depend on a responsibility orblame characteristic associated with the host vehicle or target vehicle.Accordingly, the host vehicle braking rate may be less than the targetvehicle braking rate, or vice versa.

Process 5000 may include a step 5016 for determining a stopping distancefor the target based on the target vehicle braking rate, the targetvehicle maximum acceleration capability, and the current speed of thetarget vehicle. The stopping distance for the target vehicle may be adistance that the target vehicle needs to conic to a stop, given itscurrent speed, if the target vehicle were to accelerate at its maximumacceleration capability for period of time before braking at apredetermined braking rate. For example, the stopping distance for thetarget vehicle may include an acceleration distance that corresponds toa distance the target vehicle can travel over a predetermined timeperiod at the current maximum acceleration capability of the targetvehicle, starting from the determined current speed of the targetvehicle. The distance may be determined by any means consistent withthis disclosure, including the means described above in step 5012 withrespect to the host vehicle.

Process 5000 may include a step 5018 for implementing the plannednavigational action if the planned navigation action is safe. For thepurposes of step 5018, one example of when the planned navigation actionmay be considered safe is when if the determined next-state distance isgreater than a sum of the stopping distance for the host vehicle and thestopping distance of the target vehicle. In this circumstance, therewill be no collision between the host vehicle and the target vehiclebecause the stopping distance for both of the vehicles (including thepotential distance traveled assuming maximum acceleration during thereactionary period) would allow the vehicles to come to a complete stopbefore colliding if the navigational action was performed.

For the purposes of step 5018, another example of when the plannednavigation action may be considered safe is when the determinednext-state distance is greater, by at least a predetermined minimumdistance, than the sum of the stopping distance for the host vehicle andthe stopping distance of the target vehicle. In this embodiment, thepredetermined minimum distance may be d_(rain) and may be predetermined,or determined, by any means consistent with this disclosure and have anyattribute discussed above. In some embodiments, the predeterminedminimum distance may correspond to a predetermined separation distanceto be maintained between the host vehicle and other vehicles. Forexample, a constraint of an autonomous navigation system may dictatethat the autonomous vehicle never come within (less than) a specifieddistance of other vehicles. The predetermined separation distance may bea distance of any dimension. In some embodiments, the predeterminedseparation distance is at least one meter, two meters, five meters, etc.In some embodiments, the predetermined distance may vary depending upon,for example, the speed at which the host vehicle is traveling, thelocation of the host vehicle (e.g., an urban road, a rural highway,etc.).

Navigation with a Safe Lateral Distance

As described above, RSS may be effective for determining a safe distancebetween a host vehicle and a target vehicle in a longitudinal direction.In other embodiments, however, RSS may also be used to maintain a safelateral distance between two vehicles. For example, a host vehicle and atarget vehicle may be traveling relative to one another such that theyare spaced laterally. The disclosed embodiments may be used to ensurethat a host vehicle maintains a safe lateral distance with the targetvehicle in view of one or more navigational actions that may result in achange in lateral separation between a host and target vehicle.Maintenance of a safe lateral spacing may be especially important when ahost vehicle and a target vehicle are driving next to one another. Insuch cases, unchecked lateral travel by one or more of the vehiclescould result in a collision. Safe lateral spacing, however, may also beof concern even where a host vehicle and target vehicle arelongitudinally spaced such that a continuous lateral motion by one ormore of the host vehicle and the target vehicle would not result in acollision. For example, where a lateral motion of one of the vehiclesmay cause a cut in situation such that an unsafe longitudinal distancewould result following a lateral motion by one or more of the hostvehicle and target vehicle, then there may be an interest in maintaininga certain safe lateral distance. The following sections describe variousaspects of lateral navigation in terms of lateral spacing/separation,lateral acceleration, lateral velocity, and/or lateral braking. Suchterms may refer to changes in a lateral component of motion of avehicle. For example, in a situation where a host vehicle and a targetvehicle are traveling in the same direction in adjacent lanes, if thehost vehicle steers in a manner that causes the host vehicle to approachthe target vehicle, it may be said that the lateral spacing between thehost and target vehicle decreases. This decrease in lateral spacing mayoccur at a particular lateral velocity, which may be constant or whichmay change according to a lateral acceleration value. Lateral velocitiesassociated with a decreasing lateral spacing may be designated with onesign (e.g., −), and lateral velocities associated with an increasinglateral spacing may be designated with an opposite sign (e.g., −).Lateral acceleration may refer to situations in which a host vehicle islaterally approaching a target vehicle (or laterally moving away from atarget vehicle) at an increasing lateral velocity. The term “lateralbraking” may refer to situations in which a host vehicle laterallyapproaches a target vehicle, but with a decreasing lateral velocity. Forexample, a maneuver resulting in lateral braking would cause the rate atwhich two cars are approaching one another to slow. Eventually, thelateral braking may result in a lateral velocity between the cars of 0.Maneuvers affecting lateral spacing, velocity, acceleration, etc. mayinclude steering of one or more vehicles away from or toward anothervehicle.

FIG. 51A illustrates an example scenario with two vehicles spacedlaterally from each other consistent with the disclosed embodiments, lathis scenario, a host vehicle 5102 and a target vehicle 5104 may betraveling alongside each other on a road, each in their own respectivelanes. As shown in FIG. 51A, host vehicle 5102 may perform a maneuver,such as a lane change maneuver, which reduces a lateral distance betweenhost vehicle 5102 and target vehicle 5104. The scenario shown in FIG.51A is by way of example only, and various other scenarios may arise inwhich host vehicle 5102 maintains a safe lateral distance between thetarget vehicle. For example, while host vehicle 5102 and target vehicle5104 are shown to travel in the same general direction in FIG. 51A, thevehicles may also be traveling in opposite directions with some lateralspace between the vehicles. In other instances, the vehicles may betraveling with some lateral spacing through an intersection, in aparking lot, in a merging pattern, or in other possible scenarios. Thepresent disclosure is not limited to any particular scenario in which ahost vehicle and target vehicle are traveling with some lateral spacingbetween them.

As shown in FIG. 51A, target vehicle 5104 may be traveling at a velocityrepresented by velocity vector 5124. Similarly, host vehicle 5102 may betraveling at a velocity represented by velocity vector 5123. The lateralvelocity 5123 of host vehicle 5102 may be defined as the lateralcomponent of velocity vector 5122, as shown in FIG. 51A. The lateralcomponent may be defined in various ways. For example, the lateralcomponent may use a frame of reference based on the previous headingdirection of host vehicle 5102, the current heading direction of targetvehicle 5104, the lane of travel of host vehicle 5102 and/or targetvehicle 5104, or the like. In some embodiments, lateral velocity 5123may be the component of the velocity of host vehicle 5102 that is in thedirection of target vehicle 5104. The lateral velocity of target vehicle5104 may be similarly defined as the component of a velocity of targetvehicle 5104 that is in the direction of host vehicle 5102. Any othersuitable means may be used to define the relative lateral velocity ofthe vehicles. Lateral spacing, lateral velocity, and/or lateralacceleration may be expressed in Cartesian coordinates, polarcoordinates, or according to any other suitable convention.

Host vehicle 5102 may be configured to perform a planned navigationalaction if it allows host vehicle 5102 to maintain a safe longitudinaldistance from vehicle 5104, such as an RSS safe distance, as discussedabove. The planned navigational action may be an action that decreasesthe lateral distance between host vehicle 5102 and target vehicle 5104(e.g., by increasing lateral velocity 5123). In the scenario shown inFIG. 51A, host vehicle 5102 and target vehicle 5104 may be traveling inparallel lanes with the same direction of travel and host vehicle 5012may be changing lanes into the lane occupied by target vehicle 5104.Accordingly, the planned navigational action may include a lane changemaneuver or merge maneuver. In other instances, the planned navigationalaction may include a passing maneuver, in which host vehicle 5102 ispassing target vehicle 5104 and thus may temporarily move into anadjacent lane (either in the same or opposing direction of travel) andmay move back into the lane occupied by target vehicle 5104. In otherinstances, the planned navigational action may include a turningmaneuver. For example, host vehicle 5102 may be turning at anintersection, which may reduce the lateral distance between thevehicles. The planned navigational action may include any othermaneuvers which may reduce a lateral distance between host vehicle 5102and target vehicle 5104, such as exiting a highway, maneuvering aroundan object (e.g., an obstacle in the road, a pothole, a person, etc.), aparking maneuver (e.g., parallel parking, pulling into a parking spot,etc.), or other similar actions. In some instances, it may be targetvehicle 5104 that performs the maneuver that reduces the lateraldistance between target vehicle 5104 and host vehicle 5102. The plannednavigational action of host vehicle 5102 may include a maintain forwardheading maneuver, maintain throttle action, a maintain coasting action,change heading direction, braking maneuver (lateral and/orlongitudinal), or the like.

As discussed above, the RSS safe distance may be the distance between ahost vehicle and a target vehicle at which the host vehicle may come toa stop without colliding with the target. An analog to the longitudinalRSS safe distance may include an RSS safe lateral distance between thetwo vehicles. The safe lateral distance may include a calculation of theminimum distance that it would take the vehicles to stop laterally(e.g., reduce their lateral speed to zero). In this case, rather thandetermining the vehicle's braking capacity (e.g., applying the brakes),the safe lateral distance may be based on the host vehicle's ability tosteer in a direction away from the other vehicle (or to otherwise causea lateral approach velocity of two vehicles to slow to zero). Thus, thelateral braking distance may depend, at least in part, on thesteering/turning capabilities of vehicle.

FIG. 51B illustrates an example of a host vehicle 5102 maintaining asafe lateral distance consistent with the disclosed embodiments. Targetvehicle 5104 may be traveling alongside host vehicle 5102 such that thevehicles are spaced laterally from each other. Similar to thelongitudinal safe distance described above, a processing device of bestvehicle 5102 (e.g., processing unit 110) may determine a plannednavigational action for accomplishing a navigational goal of the hostvehicle. Host vehicle 5102 may be configured to perform the plannednavigational action if an RSS safe longitudinal distance can bemaintained between host vehicle 5102 and target vehicle 5104.Additionally, host vehicle 5102 may be configured to perform the plannednavigational action if an RSS safe lateral distance can be maintainedbetween host vehicle 5102 and target vehicle 5104. As discussed above,the planned navigational action can include various maneuvers, such as alane change maneuver, a merge maneuver, a passing maneuver, a parkinglot navigation maneuver, a turning maneuver, an avoidance maneuver, amaintain forward heading maneuver, maintain throttle maneuver, or thelike. The processing device of host vehicle 5102 may determine anext-state lateral distance 5110 between host vehicle 5102 and targetvehicle 5104 corresponding to a lateral distance between the vehiclesthat would result if the planned navigational action was taken. Theprocessing device may also determine a lateral braking distance 5112 forhost vehicle 5102 and a lateral braking distance 5114 for target vehicle5104. As noted above, lateral braking distances 5112 and 5114 mayrepresent the lateral distance required for the vehicles to reduce theirlateral velocity to zero. Accordingly, the vehicles may still have anonzero overall velocity even upon laterally stopping. For example, thevehicles may continue traveling at some non-zero longitudinal velocity.The processing device of host vehicle 5102 may implement the plannednavigational action if the determined next-state lateral distance 5110is greater than a sum of lateral braking distance 5112 and lateralbraking distance 5114, thereby indicating the vehicles can both reducetheir lateral velocity (e.g., by turning) to avoid a collision. In thescenario shown in FIG. 51B, the navigational action of host vehicle 5102would be allowed as the next-state lateral distance 5110 is greater thanthe sum of lateral braking distance 5112 and lateral braking distance5114.

Consistent with the disclosed embodiments, lateral braking distance 5112for host vehicle 5102 may correspond to a distance required to achieve ahost vehicle lateral speed of zero. Lateral braking distance 5112 maydepend on at a maximum yaw rate capability of the host vehicle and themaximum change in turn radius capability of the host vehicle, startingfrom the current lateral speed of the host vehicle. Similar to themaximum acceleration rate used in the longitudinal safe distancedetermination, described above, lateral braking distance 5112 may assumea lateral acceleration of host vehicle 5102. Accordingly, determinationof lateral braking distance 5112 may assume a lateral velocity of hostvehicle 5102 after a lateral acceleration of the host vehicle as aresult of a (timing maneuver made toward the target vehicle at themaximum yaw rate capability of the host vehicle and the maximum changein turn radius capability of the host vehicle during a reaction timeassociated with the host vehicle. Constraints on the maximum yaw ratecapability and/or maximum change in turn radius capability may also beuser-defined (e.g., an occupant of an autonomous vehicle may select oneor more vehicle a setting that correspond to predetermined maximumallowable yaw rate and change in turn radius levels), scenario-defined(e.g., based on circumstances at a particular location and/or during aparticular navigation scenario), and/or based on observed performance(e.g., based on historical data collected during autonomous navigationand/or navigation by a user).

FIG. 52A illustrates an exemplary host vehicle 5102 during a plannednavigation action consistent with the disclosed embodiments. The yawrate of host vehicle 5102 may represent the rate of change in a headingangle of host vehicle 5102, for example represented as art angularvelocity, caused by turning the wheels. Host vehicle 5102 may have aheading direction 5205 at time t₁ and may have a heading direction 5206at time t₂. Heading direction 5205 may vary from heading direction 5206by an angle, Θ. The yaw rate may be represented as

$\frac{\Theta}{\left( {{t2} - {t1}} \right)}.$

In some instances, the yaw rate may be constant if the turn radius isconstant. For example, host vehicle 5102 may be turning at a constantturn radius 5207 and thus the yaw rate of host vehicle 5102 will remainconstant. The change in turn radius of host vehicle 5102 may representthe rate in which host vehicle 5102 changes the turning radius. Forexample, host vehicle 5102 may decrease the turning radius to turnradius 5208, thereby increasing the yaw rate of host vehicle 5102. Hostvehicle 5102 may also have a maximum yaw rate capability, which maycorrespond to properties of the vehicle (e.g., the turn radius when thewheel is turned all the way to one side, etc.)

Similar to the longitudinal safe distance determination previouslydiscussed, an RSS distance (e.g., a safe RSS lateral distance) bedependent upon the maximum possible lateral acceleration capability thatthe vehicle may experience during a period between an event and avehicle's reaction to sensing of the event (e.g., a reaction timeassociated with the host vehicle). Accordingly, the lateral brakingdistance may account not only for the lateral distance needed to slowthe vehicle to a lateral speed of zero, but also a worst-case scenarioof maximum lateral acceleration over a reaction time. The lateralbraking distance may include a lateral acceleration distance thatcorresponds to a lateral distance the vehicle can travel during avehicle reaction time at the vehicle's maximum yaw rate capability and amaximum change in turn radius capability for the vehicle. For example,the RSS lateral distance may account for a delay before host vehicle5102 or target vehicle 5104 begins performing a corrective steeringmaneuver. There may be several milliseconds (or more or less) betweenthe time host vehicle 5102 detects that target vehicle 5104 is movinglaterally towards host vehicle 5102 or vice versa. The processing devicemay account for the change in turn radius and yaw rate that may occurduring response period p, corresponding to the vehicle's reaction time.Response period p may correspond to a known characteristic of a vehicle,similar to the braking rate, or may be an assumed value for all cars.The lateral speed used in determining the lateral braking distance ofhost vehicle 5102 may assume a maximum yaw rate capability of hostvehicle 5102 and that host vehicle 5102 increases the yaw rate based ona maximum change in turn radius capability of the vehicle duringresponse period ρ, thereby representing a worst-case lateral brakingdistance 5112.

Referring again to FIG. 51B, the lateral braking distance 5114 fortarget vehicle 5104 may be calculated in a similar manner as lateralbraking distance 5112 for target vehicle 5102. Lateral braking distance5114 for target vehicle 5104 may correspond to a distance required toachieve a target vehicle lateral speed of zero. Lateral braking distance5114 may depend on a maximum yaw rate capability of the target vehicleand the maximum change in turn radius capability of the target vehicle,starting from the current lateral speed of the target vehicle. Lateralbraking distance 5114 may assume a lateral acceleration of targetvehicle 5104 and, accordingly, the determination of lateral brakingdistance 5114 may assume a lateral speed of host vehicle 5104 after alateral acceleration of the host vehicle as a result of a turningmaneuver by the target vehicle toward the host vehicle made at thetarget vehicle maximum yaw rate capability and the target vehiclemaximum change in turn radius capability during a reaction timeassociated with the target vehicle.

In some embodiments, the lateral speed of the host vehicle and/or thetarget vehicle may be determined based on an output of one or moresensors. For example, the lateral speed may be determined from an outputof an accelerator, a LIDAR system, a RADAR system, a GPS unit, or thelike. As another example, the lateral speed of the host vehicle may bedetermined by analyzing one or more images (e.g., based on a scalingrate change of a fixed object detected in two or more images).Similarly, the lateral speed of the target vehicle may be determined byanalyzing one or more images (e.g., based on a sealing rate change ofthe target vehicle, etc.).

For a target vehicle, the target vehicle maximum yaw rate capability andthe target vehicle maximum change in turn radius capability may bedetermined based on at least one characteristic of the target vehicle,similar to the braking capability described above with respect to thelongitudinal safe driving distance. The at least one characteristic maybe any characteristic that may correlate with a yaw rate or turn radiuscapability of a vehicle. In some embodiments, the recognizedcharacteristic of the target vehicle may include a vehicle type (e.g.,full-size sedan, compact car, SUV, crossover SUV, motorcycle, etc.), avehicle make or model, brand name, or other classifier of the targetvehicle (e.g., Toyota Prius®, BMW X5®, etc.), a vehicle size (asdescribed above with respect to the longitudinal safe driving distancedetermination), or the like. The processing device may be programmed toassume the target vehicle maximum yaw rate capability and the targetvehicle maximum change in turn radius capability based on known valuesof that vehicle type or a class of vehicles. The processing device mayuse the vehicle characteristic, for example, to access a databasecontaining known maximum yaw rate capabilities and/or maximum change inturn radius capabilities associated with each vehicle type, model, etc.The characteristic of the vehicle may be determined or identifiedthrough analysis of an image.

For host vehicle 5102, the maximum yaw rate capability of the hostvehicle and the maximum change in torn radius capability of the hostvehicle may be known or estimated by the system based on characteristicsof the vehicle, data from previous turning maneuvers, or the like. Insome embodiments, the maximum yaw rate capability of the host vehicleand the maximum change in turn radius capability of the host vehicle maybe based on predetermined constraints for the host vehicle. For example,the maximum lateral acceleration may be less than the vehicle's truemaximum capabilities but may be limited by a setting. A maximum lateralbraking rate or maximum lateral acceleration can be uncomfortable topassengers, can excessively wear down vehicle hardware (tires, brakepads etc.), or the like. Accordingly, the predetermined constraints(which may be set by system 100, a driver of host vehicle 5102, etc.)may limit the maximum yaw rates capability of the host vehicle and themaximum change in turn radius capability of the host vehicle. Theselimited values may be used in the determination of the lateral brakingdistance.

In some embodiments, at least one of the maximum yaw rate capability ofthe vehicle, the maximum change in turn radius capability of the hostvehicle, the target vehicle maximum yaw rate capability; or the targetvehicle maximum change in turn radius capability may be determined basedon one or more sensed road conditions (e.g., road material type, roadtraction properties, etc.), one or more sensed weather conditions (e.g.,rain, snow, fog, ice), or the like. For example, a processing device maydetermine maximum yaw rate capability and/or the maximum change in turnradius capability that provides the maximum safety and comfort on asnowy road, which may differ from those that would be determined for adry highway, and so forth.

In some embodiments the lateral braking rate may be based on a blame orresponsibility determination associated with host vehicle 5102 or targetvehicle 5104. From a responsibility perspective, host vehicle 5102 mayhave an obligation to steer away from target vehicle 5104, but at alower rate than target vehicle 5104. For example, target vehicle 5104may be veering into the lane of host vehicle 5102, and thus may have agreater obligation to steer away from host vehicle 5012. Accordingly,the host vehicle maximum yaw rate capability and/or maximum change inturn radius capability may be less than those of the target vehicle, orvice versa, even for the same vehicle type or model.

In some embodiments, the processing device of host vehicle 5102 may beconfigured to implement the planned navigational action if thedetermined next-state distance is greater, by at least a predeterminedminimum distance, than the sum of the lateral braking distance for thehost vehicle and the lateral braking distance of the target vehicle. Ifthe RSS safe longitudinal distance includes this minimum approachdistance component, then when the host vehicle 5102 reaches a zerolateral speed, the host vehicle should remain separated from the targetvehicle by at least the minimum approach distance. The minimum distancemay correspond to a predetermined lateral separation distance (e.g., aminimum distance of 0.5 in, 1 m, 2 m, etc.) to be maintained between thehost vehicle and other vehicles. The predetermined lateral separationmay be determined based on any set of factors consistent with thisdisclosure (e.g., a velocity associated with host vehicle 5102 and/ortarget vehicle 5104, a sensed weather condition, a user's preferences,etc.).

In some embodiments, the host vehicle may also account for thelongitudinal distance between the host vehicle and the target vehicle.FIG. 52B shows an example in which host vehicle 5202 may perform anavigation action based on both a lateral and longitudinal safe drivingdistance. Host vehicle 5202 may determine whether to perform a plannednavigation action based on a lateral distance between host vehicle 5202and target vehicle 5204. The planned navigation action may be any of themaneuvers described above, such as a lane change maneuver, a mergemaneuver, etc. The processing device of host vehicle 5202 may determinea next-state lateral distance 5210, as well as a lateral brakingdistance 5212 for the host vehicle and a target vehicle lateral brakingdistance 5214. In the scenario shown in FIG. 52B, the sum of the lateralbraking distance 5212 for the host vehicle and target vehicle lateralbraking distance 5214 may be greater than next-state lateral distance5210, indicating that the navigation action would not result in a safelateral distance from target vehicle 5204. As a result, the vehicle mayforgo the planned navigational action that would result in an unsafelateral distance.

In some embodiments, however, the processing device may be programmed toimplement the planned navigational action regardless of the next-statelateral distance (e.g., if the planned navigational action would resultin a safe longitudinal distance 5220 between the host vehicle and thetarget vehicle). In other words, in cases where a navigational actioncan be taken, and the next state distance would be greater than or equalto the safe RSS longitudinal distance, then whether the lateralseparation between a host vehicle and a target vehicle is greater thanor equal to a safe RSS lateral distance may be less relevant (e.g., thehost vehicle may be significantly forward of or behind a target vehicle,such that there is little or no risk of a lateral collision). The safelongitudinal distance may be determined in any manner consistent withthe present disclosure, including the systems and methods described indetail above. For example, safe longitudinal distance 5220 (which maycorrespond to the next-state longitudinal distance described above) maybe greater than or equal to a sum of a host vehicle longitudinalstopping distance 5222 and a target vehicle longitudinal stoppingdistance 5224. Accordingly, in the scenario shown in FIG. 52B, theprocessing device of host vehicle 5202 may perform the plannednavigation action. As discussed above, the host vehicle stoppingdistance may be based on a maximum longitudinal braking capability ofthe host vehicle and a current longitudinal speed of the host vehicle.The host vehicle stopping distance may further include a host vehicleacceleration distance corresponding to a distance the host vehicle cantravel at a maximum acceleration capability of the host vehicle during areaction time associated with the host vehicle starting from the currentlongitudinal speed of the host vehicle. Similarly, the target vehiclestopping distance may be based on a maximum longitudinal brakingcapability of the target vehicle and a current longitudinal speed of thetarget vehicle. The target vehicle stopping distance may include atarget vehicle acceleration distance corresponding to a distance thetarget vehicle can travel at a maximum acceleration capability of thetarget vehicle during a reaction time associated with the target vehiclestarting from the current longitudinal speed of the target vehicle.

FIGS. 53A and 53B include flowcharts depicting an exemplary process 5300for maintaining a safe lateral distance consistent with the disclosedembodiments. Process 5300 may be performed by at least one processingdevice, such as processing unit 110, described above. Process 5300 isexemplary only. One of ordinary skill in the art having the benefit ofthis disclosure may understand that process 5300 may include additionalsteps, exclude certain steps, or may be otherwise modified in a mannerconsistent with this disclosure.

Process 5300 may include a step 5302 for receiving at least one imagerepresentative of an environment of the host vehicle. The at least oneimage may be received from an image capture device, which may be anyimage capture device consistent with this disclosure, including imagecapture device 122. In some embodiments, the at least one image may bean image obtained from any of a camera, a RADAR, a LIDAR, or any otherdevice from which an image may be obtained, whether optical orotherwise. There may be some period of time between when the image iscaptured and when the processing device receives the image. Further,there may a period of delay between the time when an event occurs andthe imaging device captures an image of the event. For example, if atarget vehicle enters a lane in front of a host vehicle, there may be ashort period (e.g., a millisecond, 2 milliseconds, 5 milliseconds, etc.)between when the target vehicle maneuvers into the lane and when theimaging device captures an image of the target vehicle. There may alsobe time associated with analysis of the capture image, development of aplanned response based on the analysis, transmission of one or morecontrol signals to actuation systems, and an actual response of theactuation systems to the control signal(s).

Process 5300 may include a step 5304 for determining a plannednavigational action for the host vehicle. Consistent with thisdisclosure, the at least one processing device may be programmed todetermine a planned navigation action for accomplishing a navigationalgoal of the host vehicle. The navigation action may be determined basedon at least one driving policy. The planned navigation action and/or theat least one driving policy may be any consistent with this disclosure,including those discussed above. For example, the planned navigationaction may include at least one of a lane change maneuver, a mergemaneuver, a passing maneuver, a parking lot navigation maneuver, or aturning maneuver.

Process 5300 may include a step 5306 for analyzing the at least oneimage to identify a target vehicle in the environment of the hostvehicle. The at least one image may be an image received from an imagecapture device, such as image capture device 122. The at least one imagemay be the one or more images received as part of step 5302 of process5300.

Process 5300 may include a step 5308 for determining a next-statelateral distance between the host vehicle and the target vehicle thatwould result if the planned navigational action was taken. Consistentwith this disclosure, the processing device may be programmed todetermine the next-state distance between the host vehicle and thetarget vehicle. The next-state lateral distance may be calculated by anymeans disclosed herein. For example, if the planned navigation action isa lane change maneuver of the host vehicle, the next-state distance maybe a distance between the host vehicle and a target vehicle in a lanenext to the host vehicle as a result of the navigational action.

Process 5300 may include a step 5310 for determining a maximum yaw ratecapability of the host vehicle, a maximum change in turn radiuscapability of the host vehicle, and a current lateral speed of the hostvehicle. Each of these factors (i.e., the maximum yaw rate capability,the maximum change in turn radius capability, and the current lateralspeed of the host vehicle) may be determined by any means consistentwith this disclosure. The maximum yaw rate capability of the hostvehicle and the maximum change in turn radius capability of the hostvehicle may depend on the properties of the host vehicle (e.g., the turnradius of the host vehicle, tire pressure, tire wear, etc.). In someembodiments, the maximum yaw rate capability of the host vehicle and themaximum change in turn radius capability of the host vehicle are basedon predetermined constraints. For example, the maximum yaw ratecapability of the host vehicle and/or the maximum change in turn radiuscapability of the host vehicle may be constrained based on a user orsystem setting (e.g., to prevent uncomfortable lateral accelerations,prevent unnecessary wear or damage to the vehicle, etc.). Accordingly,the maximum yaw rate capability of the host vehicle and/or the maximumchange in turn radius capability of the host vehicle may depend on thecurrent speed of the host vehicle. For example, the maximum yaw ratecapability of a vehicle traveling at a first speed (e.g., 15 km/hr) maybe significantly different from the maximum yaw rate capability of thesame vehicle traveling at a second speed (e.g., 30 km/hr). In someembodiments, at least one of the maximum yaw rate capability of the hostvehicle or the maximum change in turn radius capability of the hostvehicle is determined based on a condition of a road surface (e.g., aslope of the road, a material of the road, the presence of a substanceon the road, etc.), weather conditions (e.g., snowy, humid, etc.),vehicle conditions (e.g., tire pressure, brake-pad condition, currentload of the vehicle, etc.), or the like. In some embodiments, one ormore of the factors may be determined based on an output of one or moresensors. In another example, processing device may determine a maximumyaw rate capability and/or maximum change in turn radius capabilitybased on whether the host vehicle contains, for example, one passengeror a plurality of passengers, cargo of a significant weight, a trailer,etc,

In some embodiments, the maximum yaw rate capability and/or maximumchange in turn radius capability may be determined based on one or morepredefined factors. For example, a government or industry entity mayprovide one or more regulations that dictate a maximum yaw ratecapability and/or maximum change in turn radius capability that avehicle or class of vehicles may have and the at least one processor mayassume that that the host vehicle has the vehicle braking rate and/orthe maximum acceleration capability allowed by the regulations.

Process 5300 may include a step 5312 for determining a lateral brakingdistance for the host vehicle. Consistent with this disclosure, theprocessing device may be configured to determine a lateral brakingdistance for the host vehicle based on the maximum yaw rate capabilityof the host vehicle, the maximum change in turn radius capability of thehost vehicle, and the current lateral speed of the host vehicle. Thelateral braking distance for the host vehicle may be determined by anymeans consistent with this disclosure.

In some embodiments, the lateral braking distance for the host vehiclemay correspond to a distance required to achieve a host vehicle lateralspeed of zero. The lateral braking distance may be the distance requiredto reach a lateral speed of zero at the maximum yaw rate capability ofthe host vehicle and the maximum change in turn radius capability of thehost vehicle, starting from the current lateral speed of the hostvehicle and after a lateral acceleration of the host vehicle as a resultof a turning maneuver made toward the target vehicle at the maximum yawrate capability of the host vehicle and the maximum change in turnradius capability of the host vehicle during a reaction time associatedwith the host vehicle. For example, the lateral braking distance for thehost vehicle may include a lateral acceleration distance thatcorresponds to a distance the host vehicle can travel over apredetermined time period assuming the host vehicle turns at the maximumrate towards the target vehicle. The predetermined time period may be atime period assumed by the processing device. For example, a constraintmay dictate that the processing device assumes a host vehicle willaccelerate for a certain time period (e.g., 0.5 milliseconds, 1millisecond, 2 milliseconds, 3 milliseconds, 10 milliseconds, etc.). Thepredetermined time period may be a reaction time associated with thehost vehicle. For example, the predetermined time period may be a delaybetween the time when a sensor (e.g., an imaging device) of the hostvehicle senses a condition that requires a lateral braking response fromthe host vehicle (e.g., a target vehicle coming into the path of thehost vehicle) and the time when the host vehicle begins braking at itslateral braking rate. In this example, it may be assumed that, in aworst-case scenario, the host vehicle accelerates laterally at itsmaximum capability for the entirety of the delay period. In someembodiments, the time period associated with the reaction time may bedetermined or approximated by the processing device. For example, theprocessing device may monitor the time between receiving an image anddetermining that a lateral movement response is needed. As anotherexample, the processing device may determine a mean, median, or modereaction time associated with a plurality of navigational responses anduse the mean, median, or mode reaction time when calculating a lateralbraking distance. For example, after tens, hundreds, or thousands ofnavigational responses, the processing device may determine that theaverage time between a sensed event and a navigational response is aparticular value (e.g., any real number of milliseconds) and use thatvalue as the reaction time associated with the host vehicle.

Process 5300 may include a step 5314 for determining a current lateralspeed of the target vehicle, a target vehicle maximum yaw ratecapability, and a target vehicle maximum change in turn radiuscapability. Consistent with this disclosure, the at least one processingdevice may be programmed to determine a current lateral speed of atarget vehicle. In some embodiments, the lateral speed of the targetvehicle may be determined based on the lateral speed of the hostvehicle. For example, one or more sensors on a host vehicle may provideinformation related to the speed of the host vehicle and an indicationof the acceleration or change in direction of a target vehicle inrelation to the host vehicle. In some embodiments, the target vehiclelateral speed may be determined based on analysis of at least one image.The at least one image may be, for example, the same image received bythe processing device at step 5302 that was used to identify the targetvehicle at step 5306. In some embodiments, a plurality of images may beanalyzed to determine a lateral speed of the target vehicle. Forexample, a first image may depict the target vehicle a first distancefrom the host vehicle and a second image may depict the target vehicle asecond distance from the host vehicle, the processing device may use thechange in distance and the time between the first and second images todetermine a lateral speed associated with the target vehicle. In someembodiments, the target vehicle lateral speed may be determined based onanalysis of an output from at least one of a LIDAR system or a RADARsystem associated with the host vehicle. For example, the processingdevice may use the lateral speed of the host vehicle and a distancebetween the host vehicle and the target vehicle (as sensed by, forexample, a LIDAR system) to determine a lateral speed of the hostvehicle.

In some embodiments, to account for a worst-case scenario, theprocessing device may be programmed to assume that the current lateralspeed of the target vehicle is less than or more than a sensed lateralspeed of the target vehicle. For example, if the target vehicle istraveling next to the host vehicle, the processing device may beprogrammed to reduce a sensed speed using a predetermined value, apercentage, a formula, or the like.

Consistent with this disclosure, the at east one processing device maybe programmed to assume a maximum yaw rate capability and/or a maximumchange in turn radius capability of the target vehicle based on at leastone recognized characteristic of the target vehicle. The at least onecharacteristic may be any characteristic that may correlate with amaximum yaw rate or turn radius capability. In some embodiments, therecognized characteristic of the target vehicle may include a vehicletype, class, make, model, size, or the like, as described above.

The processing device may be programmed to recognize the at least onecharacteristic from information from one or more sensors (e.g., LIDAR,RADAR, imaging devices, etc.). In some embodiments, the recognizedcharacteristic of the target vehicle may be determined based on analysisof the at least one image. For example, the image of the target vehiclemay include a text on the exterior of the target vehicle, which may beused to determine a vehicle type, vehicle model, vehicle size, or othercharacteristic. As another example, the image of the target vehicle mayinclude other objects that may be used to approximate a vehicle size orother characteristic based on comparison with the other objects. As aparticular example, a large vehicle may appear taller than a speed-limitsign whereas a small vehicle may appear shorter than a speed-limit sign.In some embodiments, the at least one characteristic of the targetvehicle may be determined based on at least one of a LIDAR output or aRADAR output. For example, a LIDAR output may include a first distanceassociated with the distance to the rear bumper of the target vehicleand a second distance associated with a distance to the front bumper orother area) of the target vehicle, the difference between which may beused to estimate the size of the target vehicle.

As discussed above, the target vehicle braking rate may correspond to amaximal or submaximal braking rate of the vehicle. The target vehiclebraking rate or target vehicle maximum acceleration capability may bedetermined by any means consistent with this disclosure, including themeans described above in step 5310 for the host vehicle. For example,the target vehicle braking rate may be determined based on a sensedcondition of a road surface, a sensed weather condition, etc. In someembodiments, the vehicle braking rate may depend on a responsibility orblame characteristic associated with the host vehicle or target vehicle.Accordingly, the host vehicle braking rate may be less than the targetvehicle braking rate, or vice versa.

Process 5300 may include a step 5316 for determining a lateral brakingdistance for the target vehicle based on the current lateral speed ofthe target vehicle, the target vehicle maximum yaw rate capability, andthe target vehicle maximum change in turn radius capability. The lateralbraking distance for the target vehicle may correspond to a distancerequired to achieve a target vehicle lateral speed of zero. The lateralbraking distance may be the distance required to reach a lateral speedof zero at the maximum yaw rate capability of the target vehicle and themaximum change in turn radius capability of the target vehicle, startingfrom the current lateral speed of the target vehicle and after a lateralacceleration of the target vehicle as a result of a turning maneuver bythe target vehicle toward the host vehicle made at the target vehiclemaximum yaw rate capability and the target vehicle maximum change inturn radius capability during a reaction time associated with the targetvehicle. For example, the lateral braking for the target vehicle mayinclude a lateral acceleration distance that corresponds to a distancethe target vehicle can travel over a predetermined time period assumingthe target vehicle turns at the maximum rate towards the host vehicle.The predetermined time period may be a time period assumed by theprocessing device to be a reaction time associated with the targetvehicle. The reaction time for target vehicle may be the same as thereaction time for the host vehicle or may be different. For example, theprocessing device may assume a reaction time based on a human driver,which may be significantly different than the reaction time associatedwith an automated vehicle.

Process 5300 may include a step 5318 for implementing the plannednavigational action if the planned navigation action is safe. For diepurposes of step 5318, one example of when the planned navigation actionmay be considered safe is when the planned navigational action if thedetermined next-state lateral distance is greater than a sum of thelateral braking distance for the host vehicle and the lateral brakingdistance of the target vehicle. In this circumstance, there will be nocollision between the host vehicle and the target vehicle because thelateral braking distance for both of the vehicles (including thepotential distance traveled assuming maximum lateral acceleration duringthe reactionary period) would allow the vehicles to steer away from eachother before colliding if the navigational action was performed.

In some embodiments, the processing device may be configured toimplement the planned navigational action if the determined next-statelateral distance is greater, by at least a predetermined minimumdistance, than the sum of the lateral braking distance for the hostvehicle and the lateral braking distance of the target vehicle. Thepredetermined minimum distance may correspond to a predetermined lateralseparation distance to be maintained between the host vehicle and othervehicles.

For example, a constraint of an autonomous navigation system may dictatethat the autonomous vehicle never come within (less than) a specifieddistance of other vehicles. The predetermined separation distance may bea distance of any dimension. In some embodiments, the predeterminedseparation distance is at least 1 m, 2 m, 5 in, etc. in someembodiments, the predetermined distance may vary depending upon, forexample, the speed at which the host vehicle is traveling, the locationof the host vehicle (e.g., an urban road, a rural highway, etc.).

In other embodiments, the processing device may be programmed toimplement the planned navigational action regardless of the next-statelateral distance if the planned navigational action would result in asafe longitudinal distance between the host vehicle and the targetvehicle, as described above with respect to FIG. 52B. For example, thesafe longitudinal distance may be greater than or equal to a sum of ahost vehicle longitudinal stopping distance and a target vehiclelongitudinal stopping distance. The host vehicle stopping distance maybe based on a maximum longitudinal braking capability of the hostvehicle and a current longitudinal speed of the host vehicle, and thehost vehicle stopping distance may include a host vehicle accelerationdistance corresponding to a distance the host vehicle can travel at amaximum acceleration capability of the host vehicle during a reactiontime associated with the host vehicle starting from the currentlongitudinal speed of the host vehicle. The target vehicle stoppingdistance may be based on a maximum longitudinal braking capability ofthe target vehicle and a current longitudinal speed of the targetvehicle, and the target vehicle stopping distance may include a targetvehicle acceleration distance corresponding to a distance the targetvehicle can travel at a maximum acceleration capability of the targetvehicle during a reaction time associated with the target vehiclestarting from the current longitudinal speed of the target vehicle.

Navigation Relative to Pedestrians at Crosswalks

The present disclosure describes a system (also referred to as anavigation system) for navigating a host vehicle in proximity to apedestrian crosswalk. The navigation system may be configured toidentify traffic lights along a roadway traveled by an autonomous orsemi-autonomous host vehicle. The navigation system may be configured toreceive information from various vehicles about locations of varioustraffic lights along the roadway, map the locations of the trafficlights on a sparse map available to the system and to the vehicles, andreceive from the vehicles information related to the traffic lights, aswell as information related to pedestrians, and crosswalks. For example,when an autonomous vehicle approaches a crosswalk, the system may beconfigured to receive information about the state of a relevant trafficlight (e.g., the traffic light includes a green light), informationwhether pedestrians are present at the crosswalk, locations ofpedestrians, their motion, their predicted future motion, and the like.

The navigation system may include multiple computing devices,processors, data storage devices, databases, and the like for efficientinformation processing. The navigation system may include non-transitorystorage devices or computer-readable media. In some embodiments, thestorage devices may include hard drives, compact discs, flash memory,magnetic-based memory devices, optical-based memory devices, and thelike. The navigation system may include one or more processorsconfigured to perform instructions that may be stored on one or morenon-transitory storage devices associated with the navigation system.The navigation system may include a distributed navigation system andvehicle navigation systems. The distributed navigation system mayinclude multiple components that may not be connected to any particularvehicle. The components may communicate via a network, which in somecases, may be a 5G network. The distributed navigation system mayinclude multiple processing computing systems located in the vicinity ofvarious roadways to reduce the network latency time associated withinformation transmission between the distributed navigation system andvehicle navigation systems. The vehicle navigation system may be part ofa vehicle control system associated with a vehicle. 1 n variousembodiments, the vehicle navigation systems and the distributednavigation system may exchange information related to any aspects ofnavigation of autonomous, semi-autonomous and/or human-operated vehiclesvia any suitable wireless communication (e.g., WiFi, 4G, 5G,communication based on visible light, infrared, microwaves, radio waves,and the like). The vehicle navigation systems and the distributednavigation system form the overall navigation system.

The navigation system (e.g., vehicle navigation systems and distributednavigation system) may determine a navigational action for the hostvehicle that may include steering, braking, or accelerating the hostvehicle. The navigational action may include parameters such as rate ofsteering, rate of braking, or rate of acceleration. The navigationalaction may include actions that may not be directly related to themotion of a vehicle. For example, such navigational actions may includeturning on/off headlights, engaging/disengaging antilock brakes,switching transmission gears, adjusting parameters of a vehiclesuspension, turning on/off vehicle warning lights, turning on/offvehicle turning lights or brake lights, producing audible signals andthe like. In various embodiments, the navigational actions are based onnavigational data available to the navigation system.

The navigational information available to the navigation system mayinclude any suitable information about various vehicles, traffic lights,traffic signals, and pedestrians in the proximity of the host vehicle.Examples of navigational information may include the position of variousautonomous and human-operated vehicles in proximity of the host vehicle,velocities of the vehicles, accelerations of the vehicles, lengths,heights, widths, and masses of the vehicles, accelerating and brakingabilities of the vehicles, predicted trajectories of the vehicles,navigational actions executed by the vehicles, locations of trafficlights, states of traffic lights, locations of crosswalks, locations oftraffic signs (including roadway surface signs), locations ofpedestrians, movements of pedestrians, and the like.

In various embodiments, the navigation system may receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle. The image capture device may be a camera for capturingvisible light. In some cases, however, the image capture device may bean infrared camera, an ultraviolet camera, microwave detecting device,LIDARs, RADARs, and the like. In various embodiments, the image capturedevice may include one or more cameras. For example, the image capturedevice may include multiple cameras that are pointing in differentdirections. The images captured by the image capture device mayrepresent the environment in front of the host vehicle, behind the hostvehicle, at the left side of the host vehicle, at the right side of thehost vehicle, the environment of a roadway in front of the host vehicle,and the like. Further, the image capture device may capture images oftraffic lights along the roadway, images of pedestrians in proximity ofroadway, images of crosswalks, and the like. In some cases, the imagecapture device may be movable (e.g., rotatable) to capture images of theenvironment of the host vehicle from at a selected azimuth and polarangle. In various embodiments, images collected from image capturedevices from different vehicles may be transmitted to a distributednavigation system for further analysis. The collected images may also bedistributed to different vehicle navigation systems.

The navigation system may detect, based on an analysis of the at leastone image, captured by the image capture device, a representation of apedestrian crosswalk in the at least one image. In an exampleembodiment, the crosswalk may be recognized in an image using anysuitable recognition technique (e.g., machine image recognitiontechnique based on neural networks). For instance, the crosswalk may berecognized by a characteristic marking of a roadway (e.g., whiterectangular regions painted on a surface of the roadway across theroadway). In some cases, crosswalk may be identified in an image basedon additional information about the location of the host vehicle. Forexample, the navigation system may determine the location of the hostvehicle and identify a crosswalk in proximity to the location of thehost vehicle. For example, the navigation system may maintaininformation about locations of crosswalks. In an example embodiment, thenavigation system may determine the location of the host vehicle, thelocation of the crosswalk and orient the image capture device tocorrectly capture the image of the crosswalk. In some cases, based onthe location of the host vehicle, and location of various other vehiclespresented in the vicinity of the crosswalk, the navigation system may beconfigured to capture images of the crosswalk from different anglesusing image capturing devices of different vehicles. The captured imagesthen may be distributed to the vehicles in the vicinity of thecrosswalk.

In some embodiments, image capture devices may be installed at thecrosswalk. For example, the image capture devices may be part of thetraffic lights, traffic signals, and the like. These devices may also beused by the navigation system to capture images of the crosswalk andtransmit images to a host vehicle navigation system located in thevicinity of the crosswalk.

In various embodiments, the navigation system may analyze one or moreimages of the crosswalk and determine, based on analysis of the images,whether a pedestrian is present at (or in the vicinity) of thecrosswalk. Pedestrians may be identified using any suitable imagerecognition technology (e.g., machine-learning techniques). In anexample embodiment, pedestrians may be identified by image capturedevices installed at a crosswalk by comparing images of a crosswalktaken at different times. For example, if at a first time an image doesnot contain a representation of a pedestrian, but at a second time animage contains a representation of a pedestrian, the navigation systemmay determine that a pedestrian is near a crosswalk. Furthermore,multiple images of a crosswalk may improve identification of apedestrian at a crosswalk. For example, multiple images of a pedestrianapproaching the crosswalk may help identify the pedestrian at acrosswalk. In various embodiments, the navigation system may determineif a representation of a pedestrian appears in the at least one imagecaptured by one or more image capturing devices.

Besides analyzing images of a crosswalk to identify pedestrians, thenavigation system may detect, based on analysis of the at least oneimage, a presence of a traffic light in the environment of the hostvehicle. The traffic lights may be detected in the environment of thehost vehicle (e.g., near a crosswalk, to the left or to the right of thehost vehicle, and the like). The navigation system may detect thepresence of the traffic light in the environment of the host vehicleusing any suitable approaches which may not necessarily be based onanalysis of images of the environment of the host vehicle. For example,the detection of the presence of the traffic light in the environment ofthe host vehicle may be based on one or more signals transmitted by thedetected traffic light. In some cases, however, a state of a detectedtraffic light may be determined based on analysis of captured images.For example, a color associated with an illuminated lamp may be detectedto determine whether a traffic light is in a stop state (e.g., red lightdetected), in a go state (e.g., green light detected), etc. The locationof lamps within a traffic light housing can also be used to determine orto indicate a state of a traffic light, as in some jurisdictions, a gostate may be associated with illumination of a lowest verticallypositioned lamp and a stop state may be associated with a highestvertically positioned lamp.

In an example embodiment, the traffic light may communicate with anautonomous vehicle using wireless communication to enable determinationof a state of the traffic light (or relevancy of the traffic light to aparticular host vehicle or to a lane of travel of the host vehicle). Thewireless communication may include one or more devices configured toexchange transmissions over an air interface to one or more networks(e.g., cellular, the Internet, etc.) using an electromagnetic field atthe radio frequency, infrared frequency, or ultraviolet frequency.Additionally, or alternatively, wireless communication may use magneticfields, electric fields, or sound. Such transmissions can includecommunications between a traffic light and an autonomous vehicle in theproximity of the traffic light, and/or in some cases, such communicationmay include communication between the traffic light and the distributednavigation system and between the distributed navigation system and thevehicle navigation system of an autonomous vehicle. It should be noted,that various other forms of communication between the traffic light andthe vehicle may be used that may include audio communication (e.g.,communication using soundwaves such as ultrasound, laser-basedcommunications and the like). In some cases, communications may includetime-dependent visible communications (e.g., the time-dependent signalproduced by LED sources).

In various embodiments, a traffic light may include a traffic lightcommunication system for generating a signal to an autonomous vehicle.For example, the traffic light communication system may include a signalgenerating module for generating a “stop” signal, a “go” signal, a“slowdown” signal, a “speedup” signal and the like. For example, the“stop” signal may indicate that the autonomous vehicle needs to stopabruptly. Such signal, for example, may correspond to a red light. The“go” signal may indicate that the vehicle needs to start or continuemoving. Such signal may correspond, for example, to a green light. The“slowdown” signal may indicate that the autonomous vehicle needs to slowdown. In some embodiments, the “slowdown” signal may include additionalparameters incorporated in information related to the signal that mayinclude the required speed for the vehicle or deceleration of thevehicle. In an example embodiment, the “slowdown” signal may correspondto yellow light. The “speed up” signal may indicate that the autonomousvehicle needs to increase its speed. In an example embodiment, thetraffic light communication system may transmit to an autonomous vehiclethe duration of time the traffic light maintains a particular state,and/or the remaining time during which the traffic light will maintain aparticular state. For example, if the traffic light is in a green state,it may transmit to the autonomous vehicle that the state will beswitched to a yellow state in thirty seconds.

In some cases, one or more autonomous vehicles may interact with thetraffic light and request state timing changes for the traffic light.For example, when there are no pedestrians at the crosswalk of aroadway, autonomous vehicles may request a traffic light to maintain itsstate by transmitting the request to the traffic light via wirelesscommunication. The navigation system may process various requests fromautonomous vehicles and adjust the state timing of the traffic light. Itshould be noted that various signals described above are illustrativeand various other signals may be incorporated as well. For example,traffic light generated signals may indicate that the vehicle needs toturn w the right, turn to the left, change lanes, or make a U turn.

In various embodiments, in addition to generating signals, the trafficlight communication system may receive navigational information fromvarious vehicles and generate signals based on the received information.For example, the traffic light communication system may receive a hostvehicle's speed and a distance of the host vehicle from the trafficlight and may generate deceleration request for the host vehicle basedon the host vehicle's speed and the distance from the traffic light.

In various embodiments, the traffic light wireless communication mayinclude various ways to authenticate communication from/to a trafficlight as well as to provide secure communication between the trafficlight and an autonomous vehicle. Additionally, or alternatively, securecommunication may be established between the autonomous vehicle and thedistributed navigation system. In an example embodiment, securecommunication may be established through the use of private and publickeys. For example, the autonomous vehicle and the distributed navigationsystem may exchange the public key for encrypting the secure informationand may use private keys for information decryption. Similarly, theautonomous vehicle may exchange public keys with the traffic lightcommunication system. In some embodiments, the traffic lightcommunication system may authenticate through the distributed navigationsystem. For example, the traffic light communication system may provideidentification and/or password information to the server of thedistributed navigation system, and the server may issue a secure tokento the traffic light communication system. In some embodiment, theserver may encrypt the secure token using the public key of the trafficlight communication system and transmit the encrypted token to thetraffic light communication system. Further, the server may beconfigured to encrypt the secure token using public key associated withan autonomous vehicle and transmit the encrypted token to the autonomousvehicle. In various embodiments, the traffic communication system mayinclude the secure token for a communication data packet transmitted tothe autonomous vehicle to provide authentication for the vehicle.Additionally, or alternatively, the traffic communication system mayinclude the secure token for a communication data packet transmitted tothe server. In a similar way, the autonomous vehicle may include thesecure token for a communication data packet transmitted to the trafficlight communication system. Additionally, or alternatively, theautonomous vehicle may include the secure token in a communication datapacket transmitted to the server. It should be noted that the securecommunication process described above is illustrative, and various otherapproaches may be used. The authenticated secure communication betweenvarious autonomous vehicles, traffic lights, and the distributednavigation system (as well as secure communication among variousautonomous vehicles) may ensure that system for navigation of variousautonomous vehicles cannot be compromised by a third party (e.g., aparty attempting to alter movements of the autonomous vehicles).

In various embodiments, the navigation system may determine whether thedetected traffic light is relevant to the host vehicle and thepedestrian crosswalk. The determination of the relevancy of the trafficlight may be based on analysis of images collected by the navigationsystem. For example, from a captured image, a particular traffic lightmay be identified above a certain lane of travel of a roadwayrepresented in the captured image. Such information can enable theprocessor(s) of the host vehicle to determine whether the detectedtraffic light is or may be relevant to the host vehicle.

Additionally, or alternatively, the relevancy of a traffic light may bedetermined using navigational information available to the navigationsystem (e.g., locations of the traffic lights, locations of crosswalks,location of the host vehicle, a vector from the host vehicle toneighboring traffic lights, and the like). In an example embodiment, therelevancy oldie traffic light to the crosswalk and the host vehicle maybe determined based on traffic light relevancy information included inone of maps accessible by the navigation system. For example, throughcrowd sourcing, identifiers associated with detected traffic lightsalong with their corresponding locations may be stored in one or moremaps (e.g., REM maps). In addition to this information, traffic lightrelevancy to certain lanes of a roadway may also be stored in the maps.This information, for example, may be based on crowdsourced informationgathered from previous drives where, for example, oars drove through anintersection using lanes 1, 2, and 3 when detected traffic lights X andY were determined to be in a green state. Of course, there are manyother examples of how vehicle behavior can be tracked and correlated totraffic light state to indicate traffic light relevancy to particularlanes of a roadway.

The relevancy of a traffic light (especially with respect to crosswalksdetected in the vicinity of a traffic light) may be determined in asimilar manner based on a detected state of the traffic light and motionof various other vehicles in the vicinity of the crosswalk. For example,if the state for a traffic light corresponds to a red light state and avehicle stops in front of the traffic light and prior to entering thecrosswalk, the navigation system may determine that the traffic light isrelevant to the crosswalk and a lane traversed by the host vehicle. Insome embodiments, the navigation system may be configured to receivevarious states corresponding to the traffic lights as well asnavigational information from various autonomous vehicles in order todetermine the relevancy of various traffic lights. For instance, a firstvehicle may communicate to the navigation system a first state for atraffic light and first navigational information associated with themovement of the first vehicle, and a second vehicle may communicate tothe navigation system a second state for the traffic light and a secondnavigational information associated with the movement of the secondvehicle. This information may be incorporated into the pool ofinformation used to construct the REM maps for a particular roadway,which can store traffic light locations along with their relevancy tolanes of travel, crosswalks, etc.

In various embodiments, a traffic light may be determined as relevant toa certain crosswalk. For example, based on image analysis a particulartraffic light may be determined to be facing the crosswalk in adirection generally perpendicular to a lane of travel of a vehicle. Insome cases, the detected traffic light may display special symbols(e.g., a symbol of a person walking, a symbol of a person standing, asymbol of a palm indicating a stop request, and the like). Thesefeatures may analyzed to identify the traffic light's relevancy to acrosswalk. This determination may be made in real time as a host vehiclenavigates and intersection to assist the host vehicle in navigatingrelative to a detected crosswalk, or it may be analyzed in apost-capture process where drive information from multiple previousdrives are collected, analyzed, and used to generate a map thatindicates traffic light relevancy. Such maps may be used by a particularhost vehicle to determine, for example, whether traffic light detectedin an image is relevant to a current lane of travel and/or whether thedetected traffic light is a pedestrian crosswalk signal relevant topedestrians navigating a crosswalk detected in an captured image. Itshould be noted that various relevancy criteria for a traffic lightdiscussed above are illustrative, and other relevancy criteria for thetraffic light that utilizes the navigation system may be used. Forinstance, in some cases, lanes of a roadway may be identified bynumerical, alphanumerical values or any other suitable identifiers bythe navigation system. The navigational system may identify the relevanttraffic light for each lane. For such cases, the determination ofrelevancy of the traffic light to the host vehicle amounts todetermining the lane for the host vehicle. In various embodiments, thenavigation system may determine the lane identifier for the lanetraversed by the host vehicle using, for example, the position of thehost vehicle, distance to the left or right curbside of the roadway, andthe like. Additionally, or alternatively, the lane may have markersrelated to its identifier positioned along the lane that may be detectedand identified by the host vehicle navigation system.

Traffic light relevancy to a particular crosswalk may also be determinedbased on previous drive information in which pedestrians were detectedin captured images walking through a particular crosswalk with aparticular nearby traffic light was in a red state. Such information mayenable a determination that when the traffic light in is in a red state,pedestrians are free to enter the crosswalk. Such information may alsosuggest that when the same traffic light is in a green state (and carsare free to pass the traffic light), that pedestrians should not enterthe crosswalk. This information can also be stored in the REM maps(e.g., as indicators of traffic light relevancy to nearby crosswalks)and used by vehicles to navigate relative to the mapped crosswalks andtraffic lights.

As discusses above, a traffic light in the vicinity of the crosswalk maybe configured to communicate with various vehicles using wirelesscommunication. For instance, the traffic light may communicate to thehost vehicle navigation system a lane identifier of a lane for which thetraffic light is relevant. The host vehicle navigation system maycompare the lane identifier received from a traffic light with the laneidentifier obtained by the host vehicle via analysis of the navigationalinformation and/or images of the crosswalk containing a representationof the traffic light. If the lane identifier received from the trafficlight matches the lane identifier obtained by host vehicle via, forexample, analysis of the images of the crosswalk or analysis of thenavigational information, then traffic light may be determined to berelevant to the host vehicle and to the crosswalk.

In various embodiments, when it is determined that one or morepedestrians appear in at least one image in the vicinity of thecrosswalk, the navigation system may determine a proximity of thepedestrian relative to the detected pedestrian crosswalk. For example,the proximity of the pedestrian may be determined by analyzing images ofthe crosswalk or a vicinity of the crosswalk. In some cases, theestimate of a distance between the pedestrian approaching the crosswalkand the curbside of the road (at which the crosswalk starts) may beimproved by analyzing multiple images and determining an averageddistance obtained by averaging different distance estimates obtainedfrom multiple images. In an alternative embodiment, the crosswalk mayinclude various sensors for detecting the presence of pedestrians andthe proximity of the pedestrians relative to the detected pedestriancrosswalk. Such sensors may include location sensors, RADAR, LIDAR, etc.The data acquired by sensors may be transmitted to the navigation systemfor further analysis and processing.

The navigation system may be configured to determine based on at leastone driving policy, a planned navigational action for causing the hostvehicle to navigate relative to the detected pedestrian crosswalk. Thedriving policy may be, for example, a set of rules/constraints fordriving an autonomous vehicle in the vicinity of a crosswalk (andelsewhere). For example, the driving policy may include guidelines fornavigating through an intersection associated with a crosswalk (e.g.,what speed to travel when navigating the intersection, how far to stayaway from pedestrians and other vehicles, where to stop relative to thecrosswalk should a stop be needed, etc.). The driving policy may alsoembody rules or guidelines for navigating relative to a detectedcrosswalk in view a state of a detected, relevant traffic light. Forexample, as noted above, a crosswalk and traffic light may be detectedbased on analysis of captured images (often in a single captured image).Relevancy of the detected traffic light to the detected crosswalk may bedetermined, for example, by accessing a REM map that stores trafficlight locations (e.g., to confirm a mapped traffic light correspondswith the image-detected traffic light) and relevancy of traffic lightsto lanes/crosswalks. Alternatively or additionally, the traffic lightrelevancy information may be determined based on relevancy informationtransmitted from the detected traffic light (or by any other suitabletechnique).

In view of a determination that a traffic light is relevant to aparticular crosswalk, the driving policy may determine appropriatenavigational actions for a host vehicle based on detected states of thetraffic light and detected states of the crosswalk. For example, suchnavigational actions may include stopping at a predetermined distancebefore the crosswalk on a red traffic light, slowing down to a firstvelocity (or maintaining a velocity of the host vehicle at a firstvelocity) when traveling through the crosswalk when the traffic light isgreen and when there are no pedestrians detected in a vicinity of thecrosswalk, and slowing down to a second velocity (e.g., slower than thefirst velocity) when the traffic light is green and there is at leastone pedestrian detected in the vicinity of the crosswalk. It should benoted, that the driving policy may depend on one or more of the type ofa crosswalk, the width of the roadway, the number of lanes on theroadway, the number of vehicles in front, behind, to the left or to theright of the host vehicle, whether the other vehicles are moving orstationary in the vicinity of the crosswalk, the estimated trajectoriesof the vehicles, the velocities of other vehicles, the type of vehicles(e.g. whether the vehicles in the vicinity of the crosswalk are large,small, slow, or fast), a presence of intersection, the number of roadsat the intersection, the number of crosswalks at the intersection, andthe like. Additionally, the driving policy may depend on one or more ofa number of pedestrians at the crosswalk, locations of pedestrians atthe crosswalk, the estimated movements of various pedestrians, theestimated trajectories of the pedestrians, and the like.

The determination of the navigational actions in the proximity of acrosswalk may be based on various factors, regardless of the drivingpolicy. In some embodiments, the navigational actions may be determinedusing a rule-based computer model, which may include a set ofinstructions implemented as software code. Additionally, oralternatively, the navigational actions may be determined using amachine-learning models, such as neural networks, generative-adversarialneural networks (GANs), information maximizing GANs (InfoGaNs), and thelike. The machine learning models may be trained using training datacollected from various sensors (e.g., image sensors for collectingimages of an environment of an example vehicle, sensors for collectingaudio data relate to the environment of the vehicle, and the like.Additionally, the training data may include navigational actionsexecuted by human drivers, or by trained machine-learning modes thatcorrespond to the images of the environment of the example vehicle. Inan example embodiment, the navigational actions for the example vehiclemay be deduced by analyzing data of various sensors of the examplevehicle, such as acceleration sensors, sensors for collectinginformation about position of a steering wheel of a vehicle, sensors forcollecting information about breaking, sensors for collectinginformation about vehicle transmission gears, and the like). Themachine-learning model then may be trained to replicate the navigationalactions executed by the human drivers base on an input of the imagesand/or audio of the environment of the example vehicle. In an exampleembodiment, the visual and audio data collected by sensors may be inputto the machine-learning model, such as a neural network, and the neuralnetwork may return as an output the acceleration data for a vehicle andthe wheel orientation of the vehicle, which may then be used to generateone or more the driving instructions for the vehicle.

In various embodiments, the determination of the planned navigationalaction may be based on the determined state of the detected trafficlight and the determined proximity of the pedestrian relative to thedetected pedestrian crosswalk. In an example embodiment, if the detectedtraffic light is green, and there are no pedestrians detected in aproximity of the detected crosswalk, the navigation system may determinea navigational action that includes traveling through the crosswalk at areduced speed, where the vehicle speed may depend on conditionsassociated with an environment of the vehicle (e.g., weather conditionsaround the vehicle, time of the day, visibility around the vehicle,whether the crosswalk is located at a busy intersection, the presence ofvehicles in the vicinity of the crosswalk, and the like). In otherwords, if the traffic light state is green and there are no pedestriansdetected near the crosswalk, it may be deduced that the host vehicle isunlikely to encounter a pedestrian entering the crosswalk before orduring a time when the host vehicle transits the crosswalk. In caseswhere the detected traffic light is green, and there is a pedestriandetected crossing the crosswalk, the vehicle may determine thenavigational action that includes slowing and stopping the vehicle. Thatis, even if the light is green, suggesting that the host vehicle has theright of way, the host vehicle should be navigated in a manner such thatthere is no risk of a collision with the pedestrian detected in thecrosswalk or entering the crosswalk. In other cases, when there is agreen light detected, but a pedestrian is also detected in proximity tothe crosswalk (e.g., within a certain predetermined distance, which maybe associated with a distance the pedestrian could potentially traveltoward the crosswalk in a time that the host vehicle takes to reachand/or traverse the crosswalk), the navigation system may determine toslow the vehicle to a safe speed, which may be selected to allow thevehicle to abruptly stop if the pedestrian is detected entering the. Insome cases, the navigational actions may include moving a vehicle into adifferent lane of a roadway to create a space between the vehicle and apedestrian detected approaching the crosswalk or standing in proximityto the crosswalk. In an example embodiment, when the detected light isred, the navigation system may determine a navigational action includingslowing and stopping the vehicle prior to reaching the crosswalk. Thus,in determining a navigational action for causing the host vehicle tonavigate relative to a detected crosswalk, the processor(s) of the hostvehicle may rely upon both a state of a detected traffic light (andwhether the detected traffic light is determined to be relevant to thehost vehicle lane of travel and/or to the detected crosswalk) andwhether pedestrians are detected in a vicinity of a the detectedcrosswalk.

In various embodiments, after determining the navigational action, thenavigation system may interact with a vehicle control system to causeone or more actuator systems of the host vehicle to implement theplanned navigational action. In an example embodiments, the actuatorsfor the host vehicle may include vehicle steering actuators (e.g.,systems responsible for steering of the host vehicle), vehicleaccelerating and braking actuators (e.g., systems responsible forbraking or accelerating the host vehicle), sound actuators (e.g.,systems responsible for making a sound), light actuators (e.g., systemsresponsible for flashing light), and the like.

An example of a roadway containing several crosswalks is illustrated inFIG. 54. FIG. 54 shows an intersection 5401, including crosswalks 5451,5452, and 5453. Intersection 5401 includes multiple lanes such as lane5403 traveled by a vehicle 5441, and lane 5404 traveled by a vehicle5442. Vehicle 5141 travels along a roadway 5413 that may include a leftcurbside (a curbside 5407) and a right curbside (a curbside 5402). Asshown in FIG. 54, intersection 5401 may have multiple traffic lightssuch as traffic lights 5430, 5432, and 5433. In an example embodiment,traffic light 5430 may include an image capture device 5460 forcapturing images of intersection 5401. In some embodiments, capturedevice 5460 may have multiple cameras for capturing various elements ofthe intersection. For example, one camera of capture device 5460 maycapture crosswalk 5451 and areas of the roadway in the vicinity ofcrosswalk 5451, a second camera of capture device 5460 may capturecrosswalk 5452 and areas of the roadway in the vicinity of crosswalk5452, a third camera may capture crosswalk 5453 and areas of the roadwayin the vicinity of crosswalk 5453. Additionally, capture device 5460 mayinclude cameras that may zoom to focus on pedestrians, such aspedestrians 5420, 5422, 5421, 5423, and 5424, take images of bicyclists(e.g., a bicyclist 5425, as shown in FIG. 54) traversing intersection5401 as well as vehicles (e.g., vehicles 5441 and 5442, as shown in FIG.54) approaching intersection 5401. In some embodiments, capture device5460 may zoom to focus on facial expressions of the pedestrians and/orcapture multiple images of the pedestrians to provide the navigationsystem with information to determine movements of the pedestrians, andthe like. In various embodiments, vehicle 5441 may have an image capturedevice 5461 and vehicle 5442 may have a respective image capture device5462 for capturing various images of intersection of 5401, as previouslydescribed. Image capture devices 5461 and 5642 may have multiple movablecameras and may capture images of different portions of theintersection, similar to image capture device 5460.

FIG. 54 shows that various pedestrians may have different abilities,velocities, expected trajectories, and the like. For example, pedestrian5422 may be determined to enter crosswalk 5451 and traverse crosswalk5451 before traffic light 5432 has a red light (i.e., the lightprohibiting the pedestrians traversing crosswalk 5451). Pedestrian 5420,on the other hand, appears to be stationary and may be unlikely to entercrosswalk 5451. Pedestrian 5424 may be a young person on a skateboard,whose motion may be unpredictable. Pedestrian 5421 may be an oldgentleman who traverses crosswalk 5453 slowly and predictably.Similarly, pedestrian 5423 is a person in a wheelchair who has limitedmobility (e.g., unlikely to rapidly change direction when traversingcrosswalk 5453). Any or all of these detected characteristics may berelied upon in determining a navigational action for the host vehicle,including, for example, a velocity at which the host vehicle is allowedto approach or traverse a crosswalk.

In various embodiments, the navigation system may include amachine-learning model for evaluating age, gender, expected movement,predictability of motion for a pedestrian identified at the crosswalk.For example, the navigation system may include a machine-learning modelthat can take, as an input, images obtained by one or more image capturedevices (e.g., devices 5460, 5461, and 5462), and return an age of apedestrian, a motion vector of the pedestrian, a location of thepedestrian, an expected trajectory of the pedestrian, an uncertaintytrajectory envelop (e.g., a trajectory envelop 5471 for pedestrian 5424,or a trajectory envelop 5472 for pedestrian 5422), and the like. Atrajectory envelope may indicate possible trajectories for a pedestrian.As can be seen in FIG. 54, trajectory envelop 5471 may be wide forpedestrian 5424 and covers crosswalk 5452 and 5453, while envelop 5472may be narrow for pedestrian 5422 and covers crosswalk 5451. Suchidentified characteristics may also be used in determining anavigational action for the host vehicle relative to a detectedcrosswalk (e.g., whether to stop the host vehicle prior to thecrosswalk, whether to slow the host vehicle, what velocity isappropriate for the host vehicle, etc. in navigating relative to thecrosswalk).

In an example embodiment, the machine-learning model may be trained byobserving movements of various pedestrians of different ages, differentsizes, different genders, different physical abilities, and the like toestablish the most probable trajectory of a given pedestrian. Inaddition to determining the most probable motion, the machine-learningmethod may also output the ranges of possible motions, the likelihood ofa most probable motion, the likelihood of possible deviations from themost probable motion and the like. In an example embodiment, ifnavigation system observers an erratic movement of a pedestrian, it mayconclude that further movement of the pedestrian may be erratic.Alternatively, the navigational system may conclude that some of thepedestrians may have a consistent motion (e.g., pedestrian 5421).

The machine-learning model described above is only illustrative, and anyother suitable approaches for predicting pedestrian motion may beemployed. For example, a rule-based approach may be used, or arule-based approach combined with the machine-learning approach may beused.

The navigation system may make an assessment of the likelihood of apedestrian entering the crosswalk prior to an intersection of thecrosswalk by the host vehicle. For example, based on the images capturedby one or more image capture devices (e.g., image capture devicesassociated with the host vehicle, with other vehicles in the vicinity ofthe crosswalk, image capture devices installed in the vicinity of thecrosswalk, and the like), the navigation system may determine if thepedestrian is approaching the crosswalk or traveling away from thecrosswalk. In some cases, the navigational system may determine possibletrajectories for pedestrians, and determine a navigational action forthe host vehicle that is statistically safe and allows the host vehicleto travel along roadway 5413. The navigational action that isstatistically safe may include an action that is estimated to be safe99% of the time if a trajectory of any one of pedestrians atintersection 5401 is unpredictable. However, the navigational action maybe determined to be significantly safer (e.g., safe 99.99999% of thetime) if trajectories of pedestrians are predictable. It should be notedthat the safety of the pedestrians depends on actions taken by thepedestrians, and roadways may not be guaranteed to be completely saferegardless of the actions of the pedestrians. The observed or predictedactions/trajectories of the pedestrian may be combined with a detectedstate of the traffic light in determining a navigational action for thehost vehicle.

In various embodiments, the planned navigational action for the hostvehicle may include traversing the pedestrian crosswalk without apedestrian-induced adjustment (i.e., any navigational action determinedto avoid a collision with a pedestrian or reduce a risk of collisionwith an pedestrian even in view of an unexpected action of thepedestrian against a state of a detected traffic light (e.g., pedestrianwalking into a crosswalk when a vehicle relevant traffic light is in agreen state—suggesting the pedestrian has a stop signal)) if thedetected traffic light is in a green state, and the determined proximityof the pedestrian relative to the detected pedestrian crosswalkindicates that the pedestrian is not likely to enter the crosswalk priorto an intersection of the host vehicle with the crosswalk. In an exampleembodiment, the host vehicle (e.g., vehicle 5441, as shown in FIG. 54)may identify the state of traffic light 5430 as it approaches crosswalk5451. If the state of traffic light 5430 is green and if no pedestriansare approaching crosswalk 5451, vehicle 5441 may not execute apedestrian-induced adjustment. In various eases, the navigational systemmay determine whether to traverse crosswalk 5451 and how to traversecrosswalk 5451 (e.g., at what speed, at what acceleration, in which laneof roadway 5413, along which trajectory, with or without the sound of ahorn or flashing of headlamps, and the like). Both decisions (i.e.,whether to traverse crosswalk 5451 and how to traverse crosswalk 5451)may depend on the observed state of the traffic light, how long thetraffic light is in the observed state, as well as the proximity ofpedestrians to crosswalk 5451. For example, if a pedestrian is detectedto be far from crosswalk 5451, vehicle 5441 may proceed according to thestate of traffic light 5430 only (e.g., green state allowing for vehicle5441 to traverse crosswalk 5451 and red state requiring vehicle 5441 tostop before reaching crosswalk 5451). In an example embodiment, if thedetected pedestrian is close to crosswalk 5451, suggesting thepedestrian could step into crosswalk 5441 (e.g., pedestrian 5422attempting to enter crosswalk 5441) and traffic light 5430 is in a greenstate, vehicle 5441 may proceed through the crosswalk, but may do so bytaking at least some cautious action relative to pedestrian 5422. Forexample, vehicle 5441 may slow down, move away from pedestrian 5422, andthe like, to minimize the risk of collision with pedestrian 5422 even ifpedestrian 5422 disobeys a pedestrian walk indicator and enters thecrosswalk. In various embodiments, if traffic light 5430 is in a greenstate and pedestrian 5422 enters any part of the crosswalk, vehicle 5441may be required to stop, regardless of the state of traffic light 5430.

The navigation system may be configured to execute a plannednavigational action that allows the host vehicle to traverse thepedestrian crosswalk (e.g., crosswalk 5451) without a pedestrian-inducedadjustment if the detected traffic light (e.g., traffic light 5430) isin a green state and the determined proximity of a pedestrian relativeto the detected pedestrian crosswalk, in combination with a detectedheading and speed associated with the pedestrian, indicates that thepedestrian cannot enter crosswalk 5430 prior to an intersection of thehost vehicle with the crosswalk. For example, if a predicted trajectoryof the pedestrian does not intersect the crosswalk, the host vehicle mayproceed to traverse crosswalk (e.g., where the pedestrian is detectedclose to the crosswalk, but walking along a sidewalk perpendicular tothe crosswalk). It should be noted, that the navigation system mayevaluate position and trajectories of any or all the pedestrians in theproximity of crosswalk 5451 in order to determine that none of thepedestrians have possible trajectories that may intersect the trajectoryof vehicle 5441.

If the navigation system determines that at least one of the pedestrians(e.g., pedestrian 5422, as shown in FIG. 54) may enter crosswalk 5451prior to an intersection of vehicle 5441 with crosswalk 5451, thenavigation system may include a planned navigational action fortraversing crosswalk 5451 with a pedestrian-induced adjustment, iftraffic light 5430 is in a green state.

In an example shown in FIG. 55A, if it is determined that pedestrian5521 may enter crosswalk 5451, vehicle 5441 may determine a plannednavigational action (e.g., a navigational action resulting in atrajectory 5502) for traversing crosswalk 5451 with a pedestrian-inducedadjustment. In an example embodiment, the pedestrian-induced adjustmentmay include deflecting trajectory of vehicle 5441 as indicated bytrajectories 5502 and 5503. For example, the pedestrian-adjustment ofthe navigational action resulting in trajectory 5503 may be due tofast-moving pedestrian 5521, and the adjustment resulting in trajectory5502 may be due to slower moving pedestrian 5521. In variousembodiments, in addition to monitoring pedestrians in the vicinity ofcrosswalk 5451, the navigational system may monitor locations andvelocities of various vehicles (e.g., vehicle 5511) traveling in thevicinity of crosswalk 5451. In an example embodiment, if vehicle 5511travels fast, the navigational system may choose trajectory 5502, andnot trajectory 5503, to avoid collision with vehicle 5503. In someembodiments, a pedestrian-adjustment may include speeding up vehicle5441, slowing or stopping vehicle 5441. For example, if pedestrian 5521has already entered crosswalk 5451, vehicle 5441 may take trajectory5504 that includes slowing down and stopping vehicle 5441, regardless ofthe state of a traffic light (e.g., traffic light 5430, as shown in FIG.54). In some cases, another possible pedestrian-adjustment may includevehicle 5441 to increase its speed and choose trajectory 5502 or 5503 topass pedestrian 5521. A pedestrian-induced adjustment may also include areduction in host vehicle speed. The magnitude of the reduction in speedmay be dependent upon a detected velocity of a pedestrian (e.g., thefaster the pedestrian moves, the more the velocity of the host vehiclemay be reduced), a predicted time the pedestrian may or could enter thecrosswalk (the shorter the time, the more the host vehicle speed may bereduced), or based on any other detected characteristic of pedestrianmovement relative to the crosswalk.

In some cases, the navigation system may execute multiplepedestrian-adjustments for multiple vehicles traveling along a roadway.For example, FIG. 55B shows vehicles 5441 and 5511 traveling alongroadway 5413 towards crosswalk 5451, while a vehicle 5512 may travel inan opposite direction, as indicated by an arrow 5531. For cases, when itis determined that pedestrian 5521 may enter crosswalk 5451, a firstpedestrian-adjustment for the navigational action for vehicle 5441 mayresult in trajectory 5524, a second pedestrian-adjustment for thenavigational action for vehicle 5511 may result in trajectory 5525, anda third pedestrian-adjustment for the navigational action for vehicle5512 may result in trajectory 5526 (e.g., vehicle 5512 steering towardsa curbside 5532 and stopping). In various embodiments, thepedestrian-induced adjustment may be determined based on a detectedheading and speed of the pedestrian. For example, the heading and speedof the pedestrian may be determined taking multiple images of thepedestrian based on one or more image capture devices (e.g., devices5460-5462, as shown in FIG. 54). In an example embodiment, as shown, forexample, in FIG. 55A, the pedestrian-induced adjustment may include alateral movement of vehicle 5441 away from the pedestrian (e.g.,movement across roadway 5413 away from pedestrian 5521, as shown bytrajectories 5502 and 5503). Additionally, or alternatively, thepedestrian-induced adjustment may include vehicle 5441 slowing downprior to the intersection of vehicle 5441 with crosswalk 5451.Additionally, or alternatively, the navigational system may requirevehicle 5441 to stop prior to the pedestrian crosswalk, even whentraffic light (e.g., traffic light 5430, as shown in FIG. 54) is in agreen state if pedestrian 5521 is detected to enter the pedestriancrosswalk.

In various embodiments, the distance of a pedestrian to a crosswalk maybe determined using geometrical calculations. For example, FIG. 55C andFIG. 55D shows examples of calculating the distance of a pedestrian to acrosswalk using image capture devices capable of motion detection. In anexample embodiment, shown in FIG. 55C, pedestrian 5421 approaches astarting location 5567 of crosswalk 5541. Image capture device 5460 mayinclude a movable camera 5565 that may include a scope 5570 for accurateorientation of camera 5565 at a point in the proximity of pedestrian5421 (e.g., a point 5571 next to shoes of pedestrian 5421, as shown inFIG. 5.5C). In some cases, movable camera 5565 may include a laser 5564that may, for example, operate using an invisible wavelength (e.g., deepblue wavelength, infrared wavelength, microwave wavelength, and thelike) and a detector for detecting a reflection spot of the laser beamfrom a surface (wherein the reflection spot is referred to as a lasermarker). The movable camera may then be oriented by placing the lasermarker in the proximity of pedestrian 5421 (e.g., at point 5571). Oncethe camera is oriented relative to starting location 5567 of crosswalk5541, angles A, and B, as shown in FIG. 55C, may be determined. As shownin FIG. 55C, image capture device 5460 is mounted on a pole 5563 and ispositioned above the surface of a crosswalk at a height H. Forparameters A, B, and H, a distance 5561 of pedestrian 5421 to startinglocation 5567 of crosswalk 5451 is determined to be H·tan(A)·sin(B).

FIG. 55D shows that a similar calculation may be made using imagecapture device 5461 associated with vehicle 5441. For device 5461located at a height H, above the surface of a roadway, with angles A,and B determining the orientation of device 5461, the distance 5561 ofpedestrian 5421 to starting location 5567 of crosswalk 5451 isdetermined to be H_(c)·tan(A_(c))·sin(B_(c)). In various embodiments,the navigation system may obtain an estimate of distance 5561 usingdifferent image capture devices and reduce the error in calculationusing distance averaging, elimination of outlier estimates, and thelike.

As described above; the navigational system may include multiplecomputing devices for executing various operations for a host vehiclenavigation. An example process 5600 of navigating the host vehicle inthe vicinity of the crosswalk is illustrated in FIG. 56. At step 5601 ofprocess 5600, a processing device of the navigation system may receive aset of images representing an environment of the host vehicle. Theimages may be taken by one or more image capture devices as describedabove. The images may include the representation of pedestrians in thevicinity of a crosswalk, images of traffic lights, traffic signs, imagesof various vehicles in the vicinity of a crosswalk, and the like.

At step 5603 of process 5600, the processing device may detect astarting and an ending location of a crosswalk. In an exampleembodiment, the crosswalk, and the starting and the ending locations ofthe crosswalk may be detected by analyzing images taken by the one ormore image capture devices. Alternatively, a location of the crosswalkmay be identified based on a map associated with the navigationalsystem. For example, the map may contain all the relevant informationabout crosswalk, and the navigation system may be configured todetermine a positioning vector from the host vehicle to the center ofthe crosswalk, a positioning vector from the host vehicle to thestarting location of the crosswalk and a positioning vector from thehost vehicle to the ending location of the crosswalk. In case of thehost vehicle approaching an intersection containing mom than onecrosswalk, multiple crosswalks may be identified on the map available tothe navigation system, with respective starting and ending locations foreach of the identified crosswalk.

At step 5605 of process 5600, the processing device may determine, basedon an analysis of at least one image obtained by one or more imagecapture devices (e.g., image capture devices 5460-5462, as shown in FIG.54) whether a pedestrian is present in the proximity of the crosswalk.In an example embodiment, as shown for example in FIGS. 55C and 55D theorientation of an image capture device (e.g., device 5460) may allowaccurate determination of distance 5561 of pedestrian 5421 to startlocation of crosswalk 5567.

At step 5607 of process 5600, the processing device may detect thepresence of a traffic light in the environment of the host vehicle. Inan example embodiment, the processing device may detect the presence ofthe traffic light using at least one image of the environment of thevehicle. For instance, the processing device may receive an image of acrosswalk (e.g., crosswalk 5451, as shown in FIG. 54), and detect, basedon a suitable image recognition algorithm, a traffic light (e.g.,traffic light 5430, as shown in FIG. 54).

At step 5609 of process 5600, the processing device may determine atraffic light relevancy (e.g., the relevancy of traffic light 5430, asshown in FIG. 54) for a vehicle (e.g., vehicle 5441, as shown in FIG.54). In an example embodiment, the relevancy of traffic light 5430 maybe determined by analyzing a correlation between the time-dependentnavigational information for various vehicles traveling along the roadsegment containing traffic light 5430 and the time-dependent stateidentifier for traffic light 5430 as described above. For example, ifthere is a direct correlation between the navigational information (orone or more changes in the navigational information) and the stateidentifier for traffic light 5430 (or changes in the state identifier),the processing device may determine that traffic light 5430 is relevantto vehicle 5441, to a lane (e.g. lane 5403, as shown in FIG. 54)traveled by the vehicle, and to crosswalk 5451, as shown in FIG. 54. Invarious embodiments, the correlation between the time-dependentnavigational information for various vehicles traveling along the roadsegment containing traffic light 5430 and the time-dependent stateidentifier for traffic light 5430 may be obtained by collectinginformation for multiple vehicles traveling along the road segment atdifferent times.

Additionally, or alternatively, if there is a direct correlation betweenthe movement of pedestrians and the state identifier for traffic light5430 (or changes in the state identifier), the processing device maydetermine that traffic light 5430 is relevant to crosswalk 5451. Forexample, when traffic light 5430 is in a state red (as observed byvehicle 5441), and pedestrians are traversing the crosswalk, and whentraffic light 5430 is in a state green (as observed by vehicle 5441),and pedestrians are waiting at starting location 5567 (as shown in FIG.55C) for the state of traffic light 5430 to change, the navigationsystem may conclude that traffic light 5430 is relevant to crosswalk5451. In various embodiments, the correlation between the time-dependentmovements of various pedestrians traversing crosswalk 5451 containingtraffic light 5430 and the time-dependent state identifier for trafficlight 5430 may be obtained by collecting information for multiplepedestrians traversing crosswalk 5451 at different times.

In some embodiments, the relevance of traffic light 5430 to crosswalk5451 and lane 5403 may be determined by referring to a map associatedwith the navigation system, where the relevance of traffic light 5430may be known/stored/represented. For instance, one or moreadministrators of the navigation system may assign an identificationnumber (ID number) to various traffic lights for a segment of a roadwayand associate their ID numbers and their locations with variouscrosswalks and lanes for the roadway segment.

At a step 5611 of process 5600, the processing device may determine astate of traffic light 5430 based on one or more images obtained byimage capture devices (e.g., devices 5460-5462, as shown in FIG. 54).The processing device may compare the images obtained for varioustraffic lights with images of various traffic lights (e.g., images oftraffic lights having a green light, red light, yellow light, etc.stored in a memory of the navigation system) to determine states ofvarious traffic lights.

Additionally, or alternatively, as described above, the state of trafficlight 5430 may be communicated to a navigational system by traffic light5430 using a wireless communication system. In various embodiments, aprocessing device may determine how much time is left until a change ofthe state of traffic light 5430. In an example embodiment, theinformation about the time left until the change of the state of trafficlight 5430 may be transmitted wirelessly by traffic light 5430, and inother embodiments, the information may be obtained by navigation systemby collecting information of states of traffic light as a function oftime by analyzing images of various vehicles traveling in the proximityof crosswalk 5430.

At step 5613 of process 5600, the processing device may determine anavigational action for the host vehicle in vicinity of the detectedcrosswalk, based on the relevancy of traffic light 5430, the determinedstate of the traffic light, a presence of the pedestrian in theproximity of the crosswalk, a shortest distance selected between thepedestrian and one of the starting or the ending location of thecrosswalk, and a motion vector of the pedestrian. As described above,the navigational action may include slowing and stopping vehicle 5441 ormoving vehicle laterally away from a pedestrian entering crosswalk 5451,or near crosswalk 5451,

At step 5615, if the navigational action is to be implemented, theprocessing device may cause one or more actuator systems associated withvehicle 5441 to implement the determined one or more navigationalactions. In various embodiments, the one or more actuator systems mayinclude regular controls for vehicle 5441 such as a gas pedal, a brakingpedal, a transmission shifter, a steering wheel, a hand brake and thelike. In some embodiments, actuator systems may be internal systems notaccessible by a human operator that perform similar functions as theregular controls accessible to the human operator. In an exampleembodiment, the processing device may be configured to causeacceleration of vehicle 5441 via an actuator system that may, forexample, include a gas pedal of a vehicle,

It should be noted that various steps of process 5600 may be modified.Additionally, or alternatively, the sequence of steps of process 5600may be modified. For example, steps 5607, 5609, and 5611 may precedesteps 5603, and 5605,

Furthermore, although the examples discussed above referred to acrosswalk visible on a road surface, the embodiments may apply to roadsin which a crosswalk is not demarcated on the road surface. For example,the disclosed embodiments may identify an intersection and therebyconsider one or more areas in a vicinity of the intersection as area(s)(e.g., potential crossing zones) from which pedestrians are likely totravel. Similarly, the disclosed embodiments may determine that acertain location (e.g., based on historical information) is an area(e.g., a potential crossing zone) from which pedestrians are likely tocross a road. This may be based on, for example, observed events in thepast (e.g., pedestrians are prone to cross the road at a particularlocation) and/or based on considerations related to a particularlocation (e.g., based on building entrances from which pedestrians mayemerge or enter).

The foregoing description has been presented for purposes ofillustration. It is not exhaustive and is not limited to the preciseforms or embodiments disclosed. Modifications and adaptations will beapparent to those skilled in the art from consideration of thespecification and practice of the disclosed embodiments. Additionally,although aspects of the disclosed embodiments are described as beingstored in memory, one skilled in the art will appreciate that theseaspects can also be stored on other types of computer readable media,such as secondary storage devices, for example, hard disks or CD ROM, orother forms of RAM or ROM, USB media, DVD, Blu-ray, 4K Ultra HD Blu-ray,or other optical drive media.

Computer programs based on the written description and disclosed methodsare within the skill of an experienced developer. The various programsor program modules can be created using any of the techniques known toone skilled in the art or can be designed in connection with existingsoftware. For example, program sections or program modules can bedesigned in or by means of .Net Framework, .Net Compact Framework (andrelated languages, such as Visual. Basic, C, etc.), Java, C++,Objective-C, HTML, HTML/AJAX combinations, XML, or HTML with includedJava applets.

Moreover, while illustrative embodiments have been described herein, thescope of any and all embodiments having equivalent elements,modifications, omissions, combinations (e.g., of aspects across variousembodiments), adaptations and/or alterations as would be appreciated bythose skilled in the art based on the present disclosure. Thelimitations in the claims are to be interpreted broadly based on thelanguage employed in the claims and not limited to examples described inthe present specification or during the prosecution of the application.The examples are to be construed as non-exclusive. Furthermore, thesteps of the disclosed methods may be modified in any manner, includingby reordering steps and/or inserting or deleting steps. It is intended,therefore, that the specification and examples be considered asillustrative only, with a true scope and spirit being indicated by thefollowing claims and their full scope of equivalents.

1. A system for navigating a host vehicle, the system comprising: atleast one processing device programmed to: receive, from an imagecapture device, at least one image representative of an environment ofthe host vehicle; determine, based on at least one driving policy, aplanned navigational action for accomplishing a navigational goal of thehost vehicle; analyze the at least one image to identify a targetvehicle in the environment of the host vehicle, wherein a direction oftravel of the target vehicle is toward the host vehicle; determine anext-state distance between the host vehicle and the target vehicle thatwould result if the planned navigational action was taken; determine ahost vehicle braking rate, a host vehicle maximum accelerationcapability, and a current speed of the host vehicle; determine astopping distance for the host vehicle based on the host vehicle brakingrate, the host vehicle maximum acceleration capability, and the currentspeed of the host vehicle; determine a current speed of the targetvehicle, a target vehicle maximum acceleration capability, and a targetvehicle braking rate; determine a stopping distance for the targetvehicle based on the target vehicle braking rate, the target vehiclemaximum acceleration capability, and the current speed of the targetvehicle; and implement the planned navigational action if the determinednext-state distance is greater than a sum of the stopping distance forthe host vehicle and the stopping distance of the target vehicle.
 2. Thesystem of claim 1, wherein the target vehicle and the host vehicle aretraveling in a parking lot.
 3. The system of claim 1, wherein the targetvehicle travels toward the host vehicle in a lane occupied by the hostvehicle.
 4. The system of claim 1, wherein the host vehicle braking ratecorresponds to a maximum braking capability of the host vehicle.
 5. Thesystem of claim 1, wherein the host vehicle braking rate corresponds toa predetermined sub-maximal braking capability of the host vehicle. 6.The system of claim 1, wherein the target vehicle braking ratecorresponds to a maximum braking capability of the target vehicledetermined based on at least one characteristic of the target vehicleidentified through analysis of the at least one image.
 7. The system ofclaim 1, wherein the target vehicle braking rate corresponds to apredetermined sub-maximal braking capability of the target vehicle. 8.The system of claim 1, wherein the host vehicle braking rate is lessthan the target vehicle braking rate.
 9. The system of claim 1, whereinthe current speed of the target vehicle is determined based on analysisof two or more of the received images representative of the environmentof the host vehicle.
 10. The system of claim 1, wherein the currentspeed of the target vehicle is determined based on an output of a RADARunit or a LIDAR unit associated with the host vehicle.
 11. The system ofclaim 1, wherein the stopping distance for the host vehicle includes ahost vehicle acceleration distance that corresponds to a distance thehost vehicle can travel during a host vehicle reaction time at the hostvehicle maximum acceleration capability, starting from the determinedcurrent speed of the host vehicle.
 12. The system of claim 1, whereinthe stopping distance for the target vehicle includes a target vehicleacceleration distance that corresponds to a distance the target vehiclecan travel during a target vehicle reaction time at the target vehiclemaximum acceleration capability, starting from the determined currentspeed of the target vehicle.
 13. The system of claim 1, wherein at leastone of the host vehicle braking rate or the target vehicle braking rateis determined based on a sensed condition of a road surface.
 14. Thesystem of claim 1, wherein at least one of the host vehicle braking rateor the target vehicle braking rate is determined based on a sensedweather condition.
 15. The system of claim 1, wherein the target vehiclemaximum acceleration capability is determined based on at least onecharacteristic of the target vehicle identified through analysis of theat least one image.
 16. The system of claim 15, wherein the at least onecharacteristic of the target vehicle includes one or more of a vehicletype, a vehicle size, or a vehicle model.
 17. The system of claim 1,wherein the planned navigational action includes at least one of a lanechange maneuver, a merge maneuver, a passing maneuver, a maintainforward heading maneuver, a parking lot navigation maneuver, or amaintain throttle action.
 18. The system of claim 1, wherein the atleast one processing device is configured to implement the plannednavigational action if the determined next-state distance is greater, byat least a predetermined minimum distance, than the sum of the stoppingdistance for the host vehicle and the stopping distance of the targetvehicle.
 19. The system of claim 18, wherein the predetermine minimumdistance corresponds to a predetermined separation distance to bemaintained between the host vehicle and other vehicles.
 20. The systemof claim 18, wherein the predetermined separation distance is at leastone meter.
 21. A method for navigating a host vehicle, the methodcomprising: receiving, from an image capture device, at least one imagerepresentative of an environment of the host vehicle; determining, basedon at least one driving policy, a planned navigational action foraccomplishing a navigational goal of the host vehicle; analyzing the atleast one image to identify a target vehicle in the environment of thehost vehicle, wherein a direction of travel of the target vehicle istoward the host vehicle; determining a next-state distance between thehost vehicle and the target vehicle that would result if the plannednavigational action was taken; determining a host vehicle braking rate,a host vehicle maximum acceleration capability, and a current speed ofthe host vehicle; determining a stopping distance for the host vehiclebased on the host vehicle braking rate, the host vehicle maximumacceleration capability, and the current speed of the host vehicle;determining a current speed of the target vehicle, a target vehiclemaximum acceleration capability, and a target vehicle braking rate;determining a stopping distance for the target vehicle based on thetarget vehicle braking rate, the target vehicle maximum accelerationcapability, and the current speed of the target vehicle; andimplementing the planned navigational action if the determinednext-state distance is greater than a sum of the stopping distance forthe host vehicle and the stopping distance of the target vehicle. 22.The method of claim 21, wherein the host vehicle braking ratecorresponds to a maximum braking capability of the host vehicle.
 23. Themethod of claim 21, wherein the host vehicle braking rate corresponds toa predetermined sub-maximal braking capability of the host vehicle. 24.The method of claim 21, wherein the target vehicle braking ratecorresponds to a maximum braking capability of the target vehicledetermined based on at least one characteristic of the target vehicleidentified through analysis of the at least one image.
 25. The method ofclaim 21, wherein the target vehicle braking rate corresponds to apredetermined sub-maximal braking capability of the target vehicle. 26.The method of claim 21, wherein the host vehicle braking rate is lessthan the target vehicle braking rate.
 27. The method of claim 21,wherein the current speed of the target vehicle is determined based onanalysis of two or more of the received images representative of theenvironment of the host vehicle.
 28. The method of claim 21, wherein thecurrent speed of the target vehicle is determined based on an output ofa RADAR unit or a LIDAR unit associated with the host vehicle.
 29. Themethod of claim 21, wherein the target vehicle maximum accelerationcapability is determined based on at least one characteristic of thetarget vehicle identified through analysis of the at least one image.30. The method of claim 29, wherein the at least one characteristic ofthe target vehicle includes one or more of a vehicle type, a vehiclesize, or a vehicle model.
 31. The method of claim 21, wherein theplanned navigational action includes at least one of a lane changemaneuver, a merge maneuver, a passing maneuver, a maintain forwardheading maneuver, a parking lot navigation maneuver, or a maintainthrottle action. 32.-80. (canceled)